We will give an overview of a residual-type a posteriori error estimation techniques applied to finite element approximations of Hodge-Laplace problems within the finite element exterior calculus (FEEC) framework. Special attention will be given to harmonic forms, their adaptive approximation, and how the quality of their approximation affects the overall error in approximating solutions to the Hodge-Laplace problem. This is joint work with Anil Hirani.