If A is an n x n matrix, you might have seen the matrix e^A in a linear algebra or differential equations class. You might not, however, have seen a matrix like |A|^e. What does this even mean? One excellent answer involves a construction known as functional calculus, which appears in numerous areas of mathematics and physics and enables the applications of scalar functions to matrices. In this talk, I plan to tell you a little bit about functional calculus and then to explore the "calculus of functional calculus," i.e., how the matrix f(A) depends on A when f is a scalar function. Time permitting, I'll say a few words about the "infinite-dimensional case" in which A is an operator on a Hilbert space. I shall assume the audience is familiar with linear algebra, multivariable (differential) calculus, and a bit of real analysis.