  Extreme value statistics (EVS) concerns the study of the statistics of the
maximum or the minimum of a set of random variables. This is an important
problem for any time-series and has applications in climate, finance, sports,
all the way to physics of disordered systems where one is interested in the
statistics of the ground state energy. While the EVS of `uncorrelated'
variables are well understood, little is known for strongly correlated random
variables. Only recently this subject has gained much importance both in
statistical physics and in probability theory. In this review, we will first
recall the classical EVS for uncorrelated variables and discuss the three
universality classes of extreme value limiting distribution, known as the
Gumbel, Fr\'echet and Weibull distribution. We then show that, for weakly
correlated random variables with a finite correlation length/time, the limiting
extreme value distribution can still be inferred from that of the uncorrelated
variables using a renormalisation group-like argument. Finally, we consider the
most interesting examples of strongly correlated variables for which there are
very few exact results for the EVS. We discuss few examples of such strongly
correlated systems (such as the Brownian motion and the eigenvalues of a random
matrix) where some analytical progress can be made. We also discuss other
observables related to extremes, such as the density of near-extreme events,
time at which an extreme value occurs, order and record statistics, etc.
