The Portable, Extensible Toolkit for Scientific computing (PETSc), which focuses on the scalable solution of problems based on partial differential equations, now incorporates new components that allow full compos ability of solvers for multiphysics and multilevel methods. Through strong encapsulation, we achieve arbitrary, dynamic composition of hierarchical methods for coupled problems and allow customization of all components in composite solvers. For example, we support block decompositions with nested multigrid as well as multigrid on the fully coupled system with block-decomposed smoothers. This paper provides an overview of PETSc's new multiphysics capabilities, which have been used in parallel applications including lithosphere dynamics, subduction and mantle convection, ice sheet dynamics, subsurface reactive flow, fusion, mesoscale materials modeling, and power networks.