We present a descriptive review of physical problems dealing with extreme values in several fields of physics. We consider different physical situations involving random variables that are correlated or not, and study the statistics of extremal variables, which is relevant for situations where height fluctuations, catastrophic events such as material failure, or power outrage occur. We describe the general theory and relate the cumulative limit distributions that can be accessible in experiments to microscopic models. In many cases however, the random variables are correlated, in interface problems for example, and the characteristics of the interaction are revealed in the asymptotic behavior of the limit distribution.