Simplified electronic structure methods like tight binding (TB) theory offer a great reduction of computational cost compared to KS-DFT, while keeping a minimal representation of the electrons which can be conveniently combined or augmented with atomic potentials or force field related models. However, the reduction in computational complexity compared to KS-DFT is offset by introducing (semi-)empirical model parameters. The challenge of obtaining parameters for many different element combinations for a wide range of applications in a chemically diverse space is addressed in the extended tight binding (xTB) Hamiltonian 5 with the corresponding geometry, frequency, and noncovalent interaction (GFN) parameterizations. Since the xTB Hamiltonian is based on KS-DFT, it has the flexibility to be adapted and improved for describing properties of interest like, e.g., spin-splittings, magnetic properties, and excited states. Furthermore, the xTB methods and their parametrizations offer the possibility to tailor the model specifically for a system of interest, thereby enhancing method performance. In this regard, reparametrization techniques, whether through classical frameworks or automated differentiation facilitate the finetuning of parameters based on existing parameterizations. It is worth noting that xTB methods are also utilized in machine learning (ML), for instance, as dataset generation tools that can be used to train more simplified models. For this, either the xTB method can be used to label data sets, or intermediate and output quantities of xTB can be used as feature inputs to models, targeting more accurate labels obtained from KS-DFT, higher levels of theory, or experiment.