In this tutorial review paper, we present our minimally invasive approach for integrating dynamically adaptive tree-structured grids into existing simulation software that has been developed for regular Cartesian grids. We introduce different physical models that we target and that span a wide range of typical simulation characteristics -- from grid-based Lattice-Boltzmann, finite volume and finite difference discretized models to particle-based molecular dynamics models. We derive the respective typical data access requirements and extensions of the algorithms to adaptively refined grids along with possible grid adaptivity criteria. In addition, after introducing basics of tree-structured adaptively refined grids, we present the adaptive grid framework p4est and our enhancement of p4est in order to provide a grid and partitioning infrastructure that can easily be used in existing simulation codes. Finally, we explain how such a grid infrastructure can be integrated into regular grid codes in general in three major steps and how we integrated p4est in the soft matter simulation package ESPResSo in particular. A summary of results fro m previously published performance and scalability studies together with new results for more realistic coupled simulation scenarios shows the efficiency and validity of the resulting new version of ESPResSo.