The study of statistical properties of dynamical systems has witnessed in recent years the development powerful new tool: the functional approach. This method focuses on how measures evolve under the dynamics, rather than on individual trajectories by analyzing the spectral properties of the transfer operator on suitable Banach spaces. In this talk, I will introduce this viewpoint in ergodic theory and illustrate its application through examples. Time permitting, I will also discuss some recent refinements of the classical theory.