in $\text{Hg}_{1-x}\text{Mn}_{x}\text{Te}$ QWs [@Budewitz2017]. One of the main focus in the research of topological materials is the realization of so-called topological superconductor (TSC) phase, with boundary states obeying non-Abelian statistics. Though at the moment there is no readily available material which is in the TSC phase (except the debated occurrence of the TSC phase in $\text{Sr}_2\text{Ru}\text{O}_4$ [@Kallin2016; @Sato2017]), it can be realized in hybrid semiconductor-superconductor systems. Many different proposals have been developed in recent years, several among them are based on DMS QWs [@Fatin2016; @Simion2018].

Most of the results obtained on 2D and bulk DMS systems in the 1990s and 2000s can be found in extensive reviews [@Dobrowolski2003; @Gaj2010], while transport studies in HgTe and PbTe QWs have been reported in Refs. [@Kvon2009; @Kvon2017] and [@Grabecki2007], respectively. In this review, we will focus mainly on experimental results and proposals published in recent years. In the first part, we will concentrate on the consequence of giant spin splitting for magnetotransport. The second part of the current review is devoted to topological phases found in chalcogenide QWs. In particular, we will review several concepts concerning the creation of Majorana states in CdTe QWs and briefly mention QSHE and QAHE in HgTe QWs. 