Are there physical challenges? Should I start working out?
You should probably start working out, but only because your health is important. And we care about you. But no, there are no athletic feats or American Ninja Warrior stunts involved. Puzzles are purely intellectual – brainteasers, if you will. Basically, we're talking about a scavenger hunt, but within the confines of a room. One solved mystery will lead to another, and another, and another, until either the clock runs out or you murder the guy who won't stop quoting National Treasure.
So, what kind of puzzles?
It really depends on the room/gamemaster, although examples include crosswords, math problems, logic games, jigsaw puzzles, color quizzes, and riddles.
Are the rooms themed?
Yep, some rooms are indeed themed. Mindquest in Budapest, for example, has a Da Vinci Code premise, while The Room in Berlin is all about the Cold War; the room is designed so that players escape from onetime East Berlin to West Berlin.
Meanwhile, Escape the Room in NYC offers three different rooms; The Agency is a James Bond-like spy HQ; The Home, which has a more Sherlock Holmes vibe; and The Office, in which players have to escape before the boss returns. So yeah, it really depends on which one you choose.