Biological networks of play a central role in the biology of cancer. Yet there remains much uncertainty regarding the connectivity of biological networks, and modifications to such connectivity in various cancers. In recent years there has been increasing interest in data-driven methods for characterizing networks of genes, proteins and metabolites. However, the complexity of these networks means that such analyses must address a number of challenging statistical issues. This tutorial will provide an introduction to the use of Markov chain Monte Carlo (MCMC) methods for learning biological networks, focusing on a class of multivariate statistical models called probabilistic graphical models. I will discuss how MCMC may be used to draw samples from posterior distributions over network structures and how such samples may be used to address questions pertaining to features of biological networks such as edges, classes of edges or paths.