Albany is a parallel C++ finite element library for solving forward and inverse problems involving partial differential equations (PDEs). In this paper we introduce PyAlbany, a newly developed Python interface to the Albany library. PyAlbany can be used to effectively drive Albany enabling fast and easy analysis and post-processing of applications based on PDEs that are pre-implemented in Albany. PyAlbany relies on the library PyBind11 to bind Python with C++ Albany code. Here we detail the implementation of PyAlbany and showcase its capabilities through a number of examples targeting a heat-diffusion problem. In particular we consider (1) the generation of samples for a Monte Carlo application, (2) a scalability study, (3) a study of parameters on the performance of a linear solver, and (4) a tool for performing eigenvalue decompositions of matrix-free operators for a Bayesian inference application.