The Ising model was one of the first spin systems (or graphical models) to be studied. Over the years, it has been used as a model for several phenomena rather different from its origins in statistical mechanics. Two important questions in many such applications are the related problems of sampling from the distribution given by the model, and the (approximate) computation of the so called "partition function" of the model. This talk will will look at methods for the deterministic approximation of the partition function of the Ising model, and its connections with notions of phase transitions in statistical physics. Based on joint work with Jingcheng Liu and Alistair Sinclair.