The Stanley-Reisner correspondence relates (non) faces of a simplicial complex with monomial ideals of a polynomial ring, yielding a number of surprising connections between the combinatorics of simplicial complexes and commutative algebra. After introducing the relevant definitions and exploring some examples, we’ll discuss Reisner’s criterion, a theorem that equates Cohen-Macaulay-ness of a certain ring with the vanishing of homology of subcomplexes of the simplicial complex.