Dark matter is one of the greatest puzzles facing physics today. Our attempts to find a dark matter particle have so far come up empty-handed, and the theoretical models that have guided these efforts for the last 30 years are increasingly suspect. We still have few clues as to its nature. In this talk, I will explore two new and complementary experimental approaches currently underway that seek evidence of a complex and hidden dark sector. Both methods rely on the hypothetical dark photon, the mediator of a new U(1) gauge symmetry similar to ordinary electromagnetism that could provide a bridge between ordinary and dark sector physics. One is a long-lived search for inelastic dark matter with the CMS detector, and the other is PADME, a fixed-target, missing-mass direct search for the dark photon. I will discuss prospects for the two experiments, experimental challenges, and perspectives for future dark matter-related new physics efforts.