PyMFEM is a Python binding layer for MFEM, the LLNL finite element method library. In practice it lets users define and solve PDE problems (Poisson, elasticity, Maxwell, DG, DPG, Navier-Stokes, topology optimization, etc.) from Python by wrapping the C++ MFEM library through SWIG. The package exposes serial (`mfem.ser`) and MPI-parallel (`mfem.par`) modules, supports Python-defined coefficients and operators via SWIG directors, includes Numba JIT acceleration for coefficient callbacks, and integrates with mpi4py, hypre, libCEED, GSLIB, GLVis, and VisIt. It is a numerical library rather than a service or data pipeline; it has no API endpoints, but it ships dozens of executable examples that serve as reproducible solver templates and also contains issue-specific regression fixtures for mesh/visualization bugs.