Abstract: Higher-order freeness extends the connection between free probability and random matrices to finer statistics of random matrices. Cumulants, quantities which exist in both classical and free probability, may also be defined in this context. In addition to providing a test for independence or freeness, cumulants facilitate the construction of free products of noncommutative probability spaces. I will discuss these higher-order free cumulants, along with their connections to random matrix quantities appearing naturally in topological expansions.