Matching problems are combinatorial optimization problems traditionally considered in the realm of computer science and combinatorics. However, when, instead of a given instance of an optimization problem, a whole class of problems is considered, according to a suitable probability distribution, methods, ideas, and tools that physicists have developed in the context of statistical mechanics of systems with frustration and disorder can be applied and have been shown to be very effective. In this talk, I will review some old and recent results obtained by the statistical physics community, and I will discuss some open problems currently under investigation.
