During the talk, I will discuss the classical Hilbert 17th problem. This problem can be divided into two smaller ones. First question is, if we have a nonnegative function, is it necessarily a sum of squares? And if it is a sum of squares, how many squares are needed? We will be mainly interested in the second problem. In particular, I will discuss recent results concerning the Pythagoras number of a ring for various rings occuring in real algebraic geometry, such as coordinate rings of a real algebraic set, rings of regular functions on an algebraic set, fields of rational functions, and possibly the rings of k-regulous functions.