Dimer models appeared first in statistical physics as models of phase transitions and in physical chemistry as objects describing packed lipids. They also have a prominent role in combinatorics, where they appear as perfect matchings on vertices of a graph connected by edges. For plane bipartite graphs they are in bijection with tilings and with stepped surfaces. Thus, random dimer configurations are in bijection with random surfaces. Remarkable feature of random dimer configurations is that local correlation functions can be computed in terms of Pfaffians of alternating adjacency matrix of a graph. This matrix is quite remarkable. In particular, if the graph can be embedded into a surface, this matrix has a natural interpretation as a discrete Dirac operator in a spin bundle over this surface. This talk is an overview of the subject. No preliminary knowledge of dimer models is required.