The Tracy-Widom distributions are a family of probability distributions that were described explicitly by Craig Tracy and Harold Widom, and shown to govern the maximal eigenvalue of large random matrices. Interestingly, they also appear in a number of other, seemingly unrelated problems such as the longest increasing subsequence of a random finite permutation, certain percolation-type models and interacting particle systems such as the totally asymmetric simple exclusion process (TASEP). I will give an overview of some results involving this distribution and, time permitting, discuss its relation to a set of conjectures concerning the so-called KPZ universality class.