After the shocking revelation that Darth Vader is Luke's father, the ending of The Empire Strikes Back might seem a bit anti-climactic. You're right—but that's actually what the filmmakers intended. The Empire Strikes Back is merely one half of the story, and you're going to have to see Return of the Jedi to witness its conclusion.

After losing the duel, his hand, and his mind, Luke throws himself from the balcony where he fought Vader and manages to grab hold of an antenna before falling to oblivion. He then telepathically contacts Leia (a hint that the pair are siblings) who picks him up in the Falcon and they escape Bespin with the Empire in hot pursuit.

From there, we see our heroes re-establishing themselves: Luke gets himself a brand new artificial hand, while Lando and Chewie take the Falcon to rescue Han from the clutches of Jabba the Hutt. That's it. After all of that non-stop tension building from the film's opening moments, we don't actually see any major plot threads resolved.

Again, this shows that this film is but the first part of a longer super-story. This is another glimpse of the influence of serialized science-fiction on Star Wars but, perhaps more importantly, it gave moviegoers a really good reason to come back in a few years and spend the dough to watch the final film in the trilogy.