Well, a civilization that old, you can make a few assumptions. As stated by you, their technology will be greatly advanced...a given. Another given is that their knowledge will be far greater than our own...note that I said KNOWLEDGE, not necessarily intelligence. Unless there are significant physiological evolutions affecting the brain (which may be possible in this case), raw intelligence and the ability to learn won't be that different than when they were when still throwing rocks, they just accumulate more knowledge over the courses of their lives due to being exposed to it.

I think to do ANYTHING with the thought, we need to make the assumption that their thought process is somewhat similar to ours, and extrapolate from that. If it isn't, then we might as well be talking about a deity rather than being for all the understanding we would have. For instance, the black monolith isn't that different from us placing an observation camera in a rain forest to see nocturnal animals in their natural state. Now, another assumption. UFO myths/legends/tales abound. Most cultures actually mention them directly or in a manner which can be easily understood to mean UFO/spacemen. Some of these tales date back thousands of years. Although this is likely a foolish assumption, we have to assume that the same people you mention are the same culture that has been watching us for all those years. Also, since there has been no direct, major change in our physiological make-up, and we don't have geneticly superior individuals among us, and there have been no "strange" new creatures appearing from nowhere, we can assume we're not just a lab. The other assumption is that they aren't going to go out of their way to destroy us unless we do something stupid which endangers them, their way of life, or their environment. Much as we treat most animals on the planet.
Now to the why. Why would they observe us for thousands of years (which for all we know could be just a few generations to them. Our own life expectancy has tripled over just the past couple hundred years due to medical advances. If they have mastered cloning and cellular regrowth, their life-spans could easily reach a thousand years.), with very limited contact.

My very uneducated guess would be that if anything other than an interesting specimen, perhaps they are attempting to understand their own development/evolution. Over the course of their existence, they would have gone through many of the same trials we as a human race have. As our technology grows, we fight to master ourselves, environment, and each other. Part of this growth is war, disease, and general pain. Much like we examine monkeys, fossils and ancient ruins for clues to the missing link and try to understand how we became the human race we know today, they may be doing to same. Or, they could just be keeping an eye on us to make sure we don't BECOME a threat...who knows.

Well, what does it really matter to us then. If they're so much more advanced than us that we can't even begin to understand, just due to the amount of development they've gone through that we haven't. We might be a bit more thinking than those monkeys in that picture, but about said alien's we're just about as knowledgeable. We might just have to accept the fact that we couldn't have any chance to co-exist with on equal terms with.

I mean, if we start chucking rocks, at the monolith, bad stuff might start to happen.

For starters, your assumptions are highly questionable. But taking them as given...

Since the UFOs are here, these aliens are obviously interested in us for something. Since they're so highly advanced, there's really no way for us to determine their motivation, or to do anything about it. We simply have to hope that their motive is to assist our advancement - like the 2001 aliens taught tool use to the monkey tribe.

The only realistic response to the interest of such a highly advanced species that refuses direct contact is to ignore them and continue on doing what we think is best for us.

I kind of feel like the answer is somewhere between the two above. It DOES depend on what these aliens have in mind when they contact us. Since we don't know and can't understand their motives (since they are more evolved than we are), we pretty much have wait and see what they want or need - and hopefully, it's not to use us like experiemental lab animals or simply destroy the human race.

And until we understand (or are made to understand, for better or worse) what they want or need, we should continue to do our best to learn all we can about our universe and the things in it!

Millions of years is actually small potatoes in evolutionary terms or astronomical terms. If there are other intelligences in the universe, they could be maybe a couple of billion years further advanced both technologically and in evolutionary terms.

The gap between them and us wouldn't be so much like the gap between humans and chimps as the gap between humans and earthworms.

What would be their interest in us, and how would they relate to us? We can't begin to imagine.

Maybe they'd look on us as we might look on a rare species of beetle. Something to study and preserve from extinction if possible.

Maybe they wouldn't be directly interested in us at all. If earthworms made up theories about things that happened in gardens, they would be earthworm-centric. They might speculate that the occasional metallic object that manifested itself in their space was a probe seeking information about them, or maybe abducting them. Little would they realise that we were planting a rose bush, or digging up weeds.

If you haven't come across it already, you might enjoy the Culture novels of Iain M Banks. His fictional galaxy is full of civilisations at all stages of development. Some have "ascended" to non-physical realms of being, and don't interact with the likes of us at all. Some try to interfere in a benign way to guide the development of primitive species. Others behave in yet other ways.

If they are so far advanced beyond us, we'll have the interesting experience of contacting a species to which, for the first time, we're not the superior ones. It could be a huge blow to our collective egos.

And who's to say they won't make contact with us at all, and just start proceedings to bulldoze us to make a galactic parking lot?

Aliens could have already visited us eg try Roswell in Mexico or Area 51
If aliens are able to travel as fast or faster than the speed of light then its sure that they are more advanced.

First off, I believe they do exist. I couldnt discount the thought that we are the only ones living in this vast universe that we're in. I've read evidences, seen videos and I believe in them. I want to experience it for myself personally and I'm just waiting for that time to come. Hopefully it would be soon. One day they'll decide to communicate with us and it would be a breakthrough. It would become a major turning point in the human race, hopefully on the positive side. We would be learning how to co-exist with them, both in their world and our own. Peace to all and beyond.

“According to an alleged briefing document, President Reagan did receive an official briefing of extraterrestrial life by his national security advisors. While debate continues over the veracity over the Reagan Briefing Document, other events point to him having received an official briefing. According to Hollywood television producer, Jamie Shandera, Reagan confided to Stephen Spielberg after a special White House film screening his knowledge of the existence of extraterrestrial life. On June 27, 1982, Reagan allegedly whispered to Spielberg after watching the movie E.T.: “You know, there aren’t six people in this room who know how true this really is." Subsequent comments throughout his Presidency concerning a possible threat by extraterrestrial life is evidence that Reagan did receive an official briefing about an extraterrestrial invasion scenario.

http://www.youtube.com/watch?v=QfQximJ-6yo

It appears that President Reagan and other public officials have been briefed in ways that led them to conclude that extraterrestrials are the enemy.

FOIA(Freedom of Information Act) documents confirm that now Secretary of Sate Hillary Clinton received a private briefing by Laurence Rockefeller on UFOs in August 1995. She then assisted Rockefeller’s efforts to get President Clinton to declassify UFO files. Whatever Hillary Clinton learned during Rockefeller’s UFO initiative, played a role in influencing her opinions about Hollywood movies of a possible extraterrestrial invasion and its unifying effects. For example, on January 14, 1999, she said:

“We will have to join together as human beings to stave off attacks from aliens in outer space, and then we’ll have to put aside our really petty differences—differences in our own country and differences among people around the world—to stand up for our common humanity.”

In other public comments, Clinton openly challenged Hollywood’s enemy stereotyping of extraterrestrial life: On June 17, 1999, for example, Clinton said:

“Many of the movies in recent years express our innate fears about what awaits us. … And often in these movies, for reasons that I question, we have space aliens who are always blowing up Washington, D.C., and the White House.”

In questioning Hollywood portrayals of extraterrestrials as enemies, Clinton was signaling her preference for a more positive view. One in which diplomatic relations with extraterrestrial life could be promoted. Nevertheless, Clinton simultaneously combined her preference for diplomacy with the possibility of an extraterrestrial invasion and its unifying effects for humanity.

The process of creating enemy images is described in Sam Keen’s, Faces of the Enemy Reflections of the Hostile Imagination. In his book, he explains how the creation of enemy images is essential for national militaries to go to war against possible future enemies. Keen’s approach is exemplified in comments by General Douglas MacArthur over an unnamed extraterrestrial enemy. In his farewell address to the U.S. Military Army on May 12, 1962, he said:

“You now face a new world, a world of change. We speak in strange terms, of harnessing the cosmic energy, of ultimate conflict between a united human race and the sinister forces of some other planetary galaxy.”

His views inspired the late Lt. Col. Philip Corso who served on MacArthur's intelligence team during the Korean War. Corso later wrote the best selling The Day After Roswell. Where he revealed his role in a secret Pentagon program to release extraterrestrial technologies. Corso believed that a vigorous space weapons program was the answer to visiting extraterrestrial life. If elements of the U.S. military does genuinely believe extraterrestrials pose a future threat, then the role of Hollywood would be crucial in conditioning the public to accept such a scenario.

http://www.youtube.com/watch?v=9zBZ8uvBmjk

Is the public being influenced by Hollywood to create enemy images of extraterrestrials? Also, are policy makers being secretly briefed, in ways that get them to promote the idea of an extraterrestrial invasion? There is testimonial evidence that an extraterrestrial invasion could be contrived to manipulate the general public. According to Carol Rosin, a former aerospace defense contractor, the extraterrestrial invasion scenario is something Dr Werner Von Braun warned her about. She claims he told her:

“Remember Carol, the last card is the alien card. We are going to have to build space-based weapons against aliens and all of it is a lie.”

In the 2008 remake of the Sci-Fi classic The Day the Earth Stood Still, the earlier self-defense actions of the robot GORT, was changed. At the end of the remake, GORT became a life destroying mechanical virus that launched an unprovoked attack on humanity to save the planet’s environment. Was the Hollywood remake yet another effort by Hollywood to condition humanity into accepting enemy images of extraterrestrial life? If policy officials have been secretly being briefed about the unifying effects of an extraterrestrial invasion, it appears that Hollywood movies are a key component of such an effort.

As of 2009 Hillary Clinton will be responsible for future diplomatic relations with extraterrestrial life. At some point, she is likely to access State Department X-Files and/or receive an official briefing on UFOs and extraterrestrial life. If as evidence suggests, extraterrestrials made diplomatic contact during the Eisenhower administration 55 years ago, then Secretary Clinton would be aware of the need to prepare the public for eventual disclosure. In doing so, she would be advised to begin an immediate public program where enemy images are abandoned. A public exopolitics debate over available evidence of the motivations of extraterrestrial life needs to begin. More constructive images of extraterrestrial life need to be vigorously promoted to counter a decades-long policy of conditioning the general public through Hollywood films and other means about fictional extraterrestrial invaders. During her visit to Indonesia, the world's most populous Muslim nation. Hillary Clinton promoted the benefits of cooperation, rather than violent conflict, between the Muslim world and the U.S. Similarly, it is best for humanity to be united by the benefits of future cooperation with extraterrestrial life, rather than reacting to a contrived extraterrestrial invasion scenario.”

Assuming they are so far advanced compared to us it still makes no sense to peek and disappear rather than just keep being undetected, especially since we are assuming they can.
Don't start telling me that we are too much behind to understand, we might lack technological discovers and knowledge but logic we do grasp.

This looks like a seen orom wily wonka and the cholate factory.