I will talk about how to calculate, or at least estimate, the Hausdorff dimension of a limsup set. Given a sequence of sets, the limsup set is the set of points that are contained in infinitely many of the sets in the sequence. Sets of this type appear for instance in metric number theory. I will concentrate however on what can be said if the limsup set is generated in a random way, which is a joint work with F. Ekström.
