Dark matter makes up most of the matter in the Universe, yet its fundamental nature remains unknown. In this talk, I will present recent high-resolution N-body simulations of self-interacting dark matter and discuss their implications for a wide range of astrophysical observations. I will highlight new signatures associated with gravothermal collapse in dark matter halos and show how they may be detected through observations of strong gravitational lensing, stellar streams, and supermassive black holes, including the JWST Little Red Dots. These studies open new avenues for uncovering the particle physics of dark matter.
