A classical result of Rademacher says that in Euclidean space Lipschitz functions are differentiable almost everywhere with respect to Lebesgue measure. In 1999 Cheeger showed that the same is true for Lipschitz functions in certain types of very general metric spaces. The question is: In this setting, what is a derivative? In the final talk we sketch a proof of Cheeger's result and discuss some its implications.