Partition monoids and their identities

So-called partition monoids arise as vector space bases of certain associative algebras which are relevant in representation theory but they also are of interest for semigroupists. We present their definitions and some recent results on their basic semigroup structure due to Mazorchuk et al. Partition monoids are equipped with a natural involution, and we proceed with studying their identities as involution monoids. The main result is that partition monoids on sufficiently large sets are non-finitely based.