The Ising model originated in statistical physics, where it was used to model magnetic objects. A classical result of Lee and Yang says that absence of zeros of the partition function implies no phase transition, i.e., analytic dependence on the parameters. More recently, it became clear that absence of zeros also implies the existence of efficient approximation algorithms. Another classical result of Lee and Yang confines the zeros of the partition function of the Ising model to the unit circle in the complex plane. In this talk I will give a precise description of the location of these zeros for the class of bounded degree graphs. This description is obtained using algorithmic techniques and ideas from complex dynamical systems. Based on joint work with Han Peters.