Computing a matching in a graph is one of "the hardest simple problems" in discrete mathematics and computer science. It is simple since most variants of matching can be solved in polynomial time, yet hard because the running times are high and the algorithms are complex. It is even more challenging to design parallel algorithms for matching, since many algorithms rely on searching for long paths in a graph, or implicitly communicate information along long paths, and thus have little concurrency. However, in the last fifteen years there has been much work in developing parallel matching algorithms via approximation: we do not find optimal matchings, but look for matchings that are guaranteed to be within a constant factor of being optimal. There has been a flurry of activity in designing and implementing such algorithms, and now we have efficient algorithms for computing matchings on multicore shared memory computers. This talk will survey this body of work in matching algorithms.