For a measure preserving dynamical system we consider the frequency of visits to a shrinking target (i.e. a sequence of sets \(A_n\), with \(meas(A_n)\) going to zero as time \(n\) goes to infinity). The distributions governing the frequency of visits can be shown to correspond to the classical extreme value distributions for i.i.d random variables. This talk will review the recent progress made in this area, with a focus on theory and applications.