The Standard Model (SM) of particle physics is an incredibly predictive theory that nonetheless leaves several fundamental mysteries unanswered, like the weakness of gravity, the nature of dark matter (DM), and the origin of the universe's matter-antimatter asymmetry. Many extensions to the SM have been proposed over the decades, including supersymmetry and WIMP dark matter, but none of their predicted signatures has been found today. I will talk about theories that extend the SM by new hidden sectors of new particles and forces, which hardly interact with us but could have similarly rich internal structure and spectra of states as the SM. These hidden sectors, including theories of Neutral Naturalness, could solve the same long-standing mysteries with radically different experimental signatures: long-lived particles and dark showers at colliders, mirror baryonic dark matter with its own rich dynamics, and alien mirror stars shining in dark light with a sprinkle of regular X-rays and optical light thrown in. These scenarios of "Dark Complexity" can be discovered but require radically different experimental approaches to standard collider and dark matter searches. This includes new detectors like MATHUSLA for the LHC and new telescope and gravitational wave searches for exotic astrophysical signatures like Mirror Stars, which can together help peel back the next layer of the fundamental physics onion and allow us to assemble a more complete understanding of the fundamental forces shaping our universe.