Since its discovery in 2005, the field of topological insulators (TIs) has experienced enormous expansion and created unforeseen activity in the solid-state physics community and beyond. Conceptually, the development of this field had its origin in the physics of the quantum Hall effect (QHE) of the two-dimensional (2D) electron gas [1,2], although today we use the topological concepts developed there to characterize also three-dimensional (3D) insulators [3]. On their surfaces, the signatures of the topology can be seen in the dispersion of the surface bands, as observed using angle-resolved photoemission spectroscopy (ARPES) and its spin-polarized angle-resolved photoemission spectroscopy (SP-ARPES) variant [4]. For the experimental verification of the quantum spin Hall effect (QSHE), however, the 2D-TIs played a vital role, and their unique transport properties are a major driving force of this field. Moreover, confining 3D topological semimetals in 2D geometries offers the possibility to open up a bandgap by size-quantization effects and create 2D TIs. A prominent example for this strategy is HgTe/CdTe quantum wells, where QSHE was observed experimentally for the first time [5].For the development of the field of TIs, the study of model Hamiltonians was definitely the first and most important theoretical tool. For many semiconductors, specialized ⋅ Hamiltonians were developed from the late 1950s, which describe the electronic structure near the bandgap with high precision. But after the experimental realization of 3D TIs comprised of different elements, density functional theory (DFT) calculations became increasingly important to describe the bulk and surface bandstructures of whole families of compounds, to investigate their topological properties. Also for 2D TIs, there are questions that are most conveniently addressed within DFT, for example, issues of structural stability, interactions with substrates, and other effects that are difficult to embody into a model Hamiltonian with sufficient accuracy.