Throughout the series, Beckett leaps into various people, trying to change their lives for the better. As a side-effect of the time travel, he acquires partial amnesia so he does not remember prior leaps or even details of his own life.

Beckett's only contact with his original time is Al Calavicci (Dean Stockwell), who appears as a hologram with a mobile computer called Ziggy. Nobody can see or hear Al but Beckett, making for some humorous scenes where it looks as though Beckett is talking to himself in every episode.

With Al as a guide to Beckett's "missions" on each leap, the two travel from one person's life to the next, hoping that the next leap will take Beckett back home. There have been instances where the two switched places, which permitted Beckett a chance to return to his time, but he always returned to take Al's place.

Much to the dismay of loyal fans (who have given the show a cult following since it went off the air), the last episode of the series informs them that Beckett, in fact, never leaps home.