Astrophysical observations spanning dwarf galaxies to galaxy clusters indicate that dark matter densities in their central regions are much more diverse than predicted in the prevailing cold dark matter theory. In this talk, I will show that self-interacting dark matter can provide a unified solution to a number of puzzles in astronomy and astrophysics, including the diverse rotation curves of spiral galaxies, dark matter distributions in Milky-Way satellite galaxies and ultra-diffuse galaxies, and density cores in galaxy clusters.