Among the multiples applications of Bernstein polynomials there is one related to the processing of random signals, originally introduced by John von Neumann in 1956. Thanks to advances in technology, some ideas from the late sixties of the last century have been retaken in order to design implementations which allow -in certain cases- a simpler and more efficient processing than the traditional one. In this descriptive review article we will illustrate the use and importance of Bernstein polynomials in solving problems associated with stochastic computing, taking as a starting point the notion of stochastic logic in the sense of Qian-Riedel-Rosenberg.