We discuss dimension theory in the class of all topological groups. For locally compact topological groups there are many classical results in the literature. Dimension theory for non-locally compact topological groups is mysterious. It is for example unknown whether every connected (hence at least 1-dimensional) Polish group contains a homeomorphic copy of [0,1]. And it is unknown whether there is a homogeneous metrizable compact space the homeomorphism group of which is 2-dimensional. We discuss several classical problems for nonmetrizable topological groups. Some of these problems may end up in set theory.