Finite element methods are numerical methods that approximate solutions to PDEs using piecewise polynomials on a mesh representing the problem domain. Adaptive finite element methods are a class of finite element methods that selectively refine specific elements in the mesh based on their predicted error. In order to establish the viability of an AFEM, it is essential to know whether or not that method can be proven to converge. In this talk I will present a general framework that would establish convergence for an AFEM and apply the framework to specific problems.