We will discuss construction, analysis and adaptive time-stepping of time-splitting schemes applied in large-scale simulations of quantum systems. Local error estimates are either based on the defect of the numerical solution or an embedding idea. For highly nonlocal nonlinear potentials arising in model reductions such as the multi-configuration time-dependent Hartree-Fock (MCTDHF) method, these turn out to be outperformed by exponential Lawson-multistep schemes. Hence methods of the latter class will also be equipped with error estimators and tested in particular with respect to their long-time stability.