One of the most recent mathematical applications of Sampling Theory is in the field of Special Functions, where sampling theorems have been proved to be a very useful tool in summing infinite series. The main aim of this chapter is to report on some advances in this direction. We will show how sampling theorems can be used to derive numerous summation formulae, some of which we believe to be new. Among all available methods to sum up infinite series, the sampling theory technique is the easiest and the most straightforward.