In this talk I will describe a correspondence between dimer model on planar bipartite graphs and circle pattern embedding of these graphs, that is, embeddings of these graphs so that each face is cyclic. This correspondence is the key for studying Miquel dynamics, a discrete integrable system on circle patterns. Time permitting, I will explain how Tutte embeddings for resistor networks and s-embeddings for Ising models arise as special cases. This is joint work with Richard Kenyon (Yale University), Wai Yeung Lam (University of Luxembourg) and Marianna Russkikh (MIT).