Self-interactions of dark matter could solve the “small-scale problems” of the cold dark matter paradigm. They are ubiquitous when dark matter is part of dark sectors. Self-interacting dark matter halo experiences the gravothermal evolution: the central halo firstly develops a core but ultimately collapses to a cuspy profile. The presence of the collapsed phase greatly diversifies the distributions of dark matter halos and leads to several unique observational signatures. Nevertheless, the collapse process takes time far exceeds the age of the Universe to develop for purely elastic dark matter self-interactions with a constant cross-section strength around O(1 cm^2/g), a benchmark to explain the galactic observations. The collapse process can be greatly accelerated for dark matter with self-interactions beyond elastic interactions, or dark matter halos with environmental effects that enhanced the heat outflow. We investigated two scenarios leading to an accelerated collapse process: (1) a mild dissipative dark matter self-interaction and (2) dark matter halos with a compact central baryonic component. For the first scenario, we derived new constraints on the dissipative self-interactions using near-field dwarf galaxy data. Based on the second scenario, we proposed a new mechanism to seed supermassive black holes observed at redshifts > 6-7, a growing puzzle in astrophysics.