Everything you wish to know about correlations but are afraid to ask

We discuss the various definitions of time correlation functions and how to estimate them from experimental or simulation data. We start with the various definitions, both in real and in Fourier space, and explain how to extract from them a characteristic time scale. We then study how to estimate the correlation functions, i.e.\ how to obtain a good approximation to them from a sample of data obtained experimentally. Finally we discuss some practical details that arise in the actual computation of these estimates, and we describe some relevant algorithms.