The existence of a nonzero permanent electric dipole moment (EDM) requires the violation and parity and time-reversal invariance, or equivalently CP invariance. New sources of CP violation are expected in particle physics; in particular, they are thought to be required to explain the dominance of matter over antimatter in the Universe. EDM experiments are thus complementary to searches for CP violation with antiparticles at high-energy colliders. Recently, an improved bound on the EDM of the electron was reported [T. S. Roussy et al., Science 381, 46 (2023)]. The authors claim that their "results provide constraints on broad classes of new physics above 10^13 electon volts, beyond the reach of current particle colliders or those likely to be available in the coming decades". The measurements were done in a table-top-scale setup with ions of hafnium-fluoride molecules in a trap. In this talk, I will assess these extraordinary findings in the context of the landscape of ongoing experiments that search for the EDMs of the neutron, atoms, and molecules. I will discuss theoretical efforts to interpret such EDM experiments on composite hadronic or atomic systems in terms of the underlying sources of CP violation. Throughout, I will offer some opinions about where things stand and what is needed in the coming years.