A main goal of algebraic geometry is the classification of algebraic varieties and a central tool in this endeavor is the study of moduli spaces. I will discuss the moduli space of plane curves of degree d: a parameter space where each point corresponds to an isomorphism class of a certain curve. There are many techniques to compactify this space, including GIT, the minimal model program, and a differential geometric approach called K stability. In joint work with K. Ascher and Y. Liu, we interpolate between these different compactifications and study the problem via wall crossings.