The search for Electric Dipole Moments (EDMs) of fundamental quantum systems is ongoing since the 1950’s: an EDM would be a manifestation of physics at very high energy scales, and would violate P and T symmetry. It has significant impact on our understanding of the early Universe, in particular the origin of matter-antimatter asymmetry. Key for measurements was the invention of Ramsey’s method of separated oscillating fields, which is not only the basis for atomic clocks, but also for most measurements in this field of research. It allowed for unprecedented experimental sensitivities, e.g. 10^-44 J energy resolution in 129-Xe. Many different systems like nucleons, atoms or leptons are experimentally accessible and complementary in physics reach. Through relating results from different experiments using effective field theory with each other and also to measurements at higher energy scales, EDM searches are among the most powerful tools in particle physics. An overview of the field with current status of joint analyses, as well as a selection of particularly interesting experimental approaches and strategies, with lots of future potential will be discussed, including neutron, proton and 129-Xe/3-He spin clocks. As some of the most precise experiments of mankind based on extremely sensitive quantum-sensing technologies developed for this purpose, direct spin-offs are e.g. searches for ultra-light axion Dark Matter, but also applications that currently deliver groundbreaking new insights in the functionality of the human heart.