A dimer ABC

We give an overview of recent developments in the theory of dimer models. The viewpoint we take is inspired by mirror symmetry. After an introduction to the combinatorics of dimer models, we will first look at dimers in dynamical systems and statistical mechanics, which can be viewed as coming from the A-model in mirror symmetry. Then we will discuss the role of dimers in the theory of resolutions of singularities, which is inspired by the B-model. The C stands for the connections that tie both subjects together: clusters, categories, and stability conditions. In this final part we will give some ideas on how these two stories fit in a broader framework.