2HDM-based and SUSY-inspired models

Models with an extended Higgs sector, such as two-Higgs-doublet models (2HDMs), have traditionally played an important role in DM searches with supersymmetry as a prime example of a complete theory that addresses the nature of particle DM. In addition, UV-complete simplified models based on 2HDMs, such as the 2HDM with a pseudoscalar mediator investigated at the LHC, gain increasing attention. This talk will review the constraints on SUSY and general 2HDM-based WIMP DM from collider searches, with an emphasis on the complementarity of collider with direct (DD) and indirect detection (ID) results. Rather than highlighting individual analyses and constraints, it will focus on regions of parameter space that cannot easily be probed by collider experiments and for which a re-interpretation of DD/ID results is particularly well motivated. Finally, an outlook on SUSY- and 2HDM-inspired DM searches in Run 3 (gains from statistically limited channels, systematics-related limitations, ...) will be given.