Most of the distribution functions in the universe, including those for mass, energy, and structure of components like dark matter, galaxy clusters, galaxies, magnetic fields, cosmic rays, star clusters, and stars, have power-law shapes suggesting a lack of definite scales in their formation processes. As these scale-free behaviors are obtained without fine-tuning, they are by definition self-organized, which raises fascinating questions regarding the respective roles of long-range (gravity) and short-range (collisional) interactions. These questions touch on the interaction between dark matter, baryons, cosmic rays and magnetic fields, the importance of scales where the power-laws break down, the observed deviations from power-laws, and the range of scales that are truly coupled. Computer simulations now include a large enough range of scales to reproduce some of these power-laws, and recent theoretical analyses attempt to unify them.