Cosmic gamma rays are a valid probe to search for fundamental physics. Some of these exotic and exciting scenarios are the subject of this contribution to the book. All current Imaging Atmospheric Cherenkov Telescopes (IACTs) have invested a great deal of time and resources in scouting these out. In this chapter, we focus on the case of indirect search for weakly interacting massive particles (Sec. 8.1) and that of search for axion-like particles (Sec. 8.2). We continue with less debated, yet interesting studies on the search for primordial black holes (Sec. 8.3), tau-neutrinos (8.4), and magnetic monopoles (8.5). Other scenarios of fundamental physics like the search for Lorentz Invariance violations are treated elsewhere in the book. We structured the contribution providing a self-contained (yet minimal) theoretical framework, as well as a complete report of all IACTs' published contribution to the topics under consideration. Our aim is to provide a reference review as well as take a photograph of the effort of the current generation of IACTs and the challenges taken, in preparation of the next-generation instrument to come, the Cherenkov Telescope Array.