99 problems and presentations are most of them

Geometric (even combinatorial) group theory suffers from the unfortunate situation that many obvious questions about group presentations (ex: is this a presentation of the trivial group? is this word the identity in that group?) cannot be answered. Not only "we don't know how to tell" but "we know that we cannot know how to tell" - this is called undecidability. This talk will serve as an introduction (for non-experts, since I am also such) to the area of group theoretic decision problems: I'll aim to cover some problems, some solutions (or half-solutions) and some of the general sources of undecidability, as well as featuring some of my (least?) favourite pathological groups.