Translating the computing power of high-performance computing systems into simulation performance requires new parallel algorithms due to the rapid increase in core counts. For time-dependent partial differential equations, parallel-in-time methods like Parareal can provide additional concurrency on top of already widely used spatial parallelization. Parareal, as well as related methods like MGRIT or PFASST, iterate on a hierarchy of levels (from fine to coarse) and "shift" the natural serial dependency of time stepping to the coarsest and cheapest level, thus allowing the costly fine level computation to be done in parallel. Efficiency depends on having a cheap coarse level model but also rapid convergence. These two aims compete: a cheaper coarse model will be less accurate and may lead to slower convergence. Using a lower spatial resolution on the coarse level is attractive as it gives a more significant reduction in computational cost than using a coarse time step. However, this needs to be weighed against potentially slower convergence. I will show some recent theoretical and numerical results to illustrate the impact of spatial coarsening on Parareal convergence.