Persistent homology studies which homological features of a topological space persist over a long range of scales. I will discuss two applications of this formalism to the study of vacua in string theory. In the first application, I will discuss how to adapt such techniques to address the presence/absence of structure in a series of string compactifications (for example flux vacua in type IIB or heterotic vacua). In the second application, I will address the problem of studying vacua of certain two-dimensional Landau-Ginzburg models and see what information we can get about their algebraic structures.