In this presentation, we discuss recent progress and ongoing open questions in space-time modeling, their discretization and numerical solution of coupled problems. Under the terminology coupled problems, we understand nonstationary, nonlinear, coupled PDE system and variational inequalities (CVIS). First, we have made progress in goal-oriented a posteriori error control and adaptivity with the dual-weighted residual method for incompressible flow (Navier-Stokes equations) and fluid-structure interaction. Second, we extended those concepts to space-time model order reduction with application to porous media problems, so far prototype benchmarks such as Mandel's problem. Third, ongoing discussions with engineering colleagues yield new concepts in space-time variational material modeling, satisfying thermodynamical principles and internal variables, based on Hamilton's principle, in which open questions, specifically to us, the mathematical community, persist.