For systems of PDEs, block preconditioning techniques are widely used to solve the linear(ized) system of equations that arise at each (sequential) time step, or for a steady state solution. Convergence of 2x2 block preconditioned fixed-point and Krylov iterations is fully determined by the preconditioning of the underlying Schur complement. In practice, many block preconditioners are developed through some assumptions of approximate commutation of differential operators to form an approximate Schur complement that is relatively easy to invert. This talk introduces the framework of space-time block preconditioning, extending the concepts of approximate commutation used in spatial block preconditioning to the space-time setting. In doing so, we can reduce the iterative solution of space-time systems of PDEs to the solution of a single-variable space-time equation, and corresponding Schur complement approximation. Space-time multigrid and algebraic multigrid methods have already demonstrated significant speedup over sequential time stepping for the former, and, with careful construction, the latter can be straightforward to compute in parallel as well. We demonstrate the principles of space-time block preconditioning applied to the incompressible Navier Stokes equations and the incompressible MHD equations. Theoretical motivation is provided for the new methods, and its robustness and scalability is shown on multiple model problems. More broadly, space-time block preconditioning offers a path to the fast, parallel, space-time solution of systems of PDEs, through the simpler task of solving single-variable space-time equations.