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Despite being discovered over 86 years ago, fission still lacks a complete microscopic description, making it one of the oldest problems in quantum many-body theory. For comparison, superconductivity was discovered in 1911 and described microscopically in 1957 by the BCS theory. Fission is particularly difficult to treat theoretically in a unified manner as it contains many qualitatively distinct processes, each of which occurs at vastly different timescales, from the entrance channel (such as neutron absorption) to the splitting of a deformed nucleus into two fragments to the subsequent emission of radiation (typically gamma rays and neutrons). In 2016, the first simulation of the most rapid and highly non-equilibrium stage of fission, the evolution of the compound nucleus from the outer saddle point to scission to the formation of two fully separated fission fragments (FFs), was achieved for realistic initial conditions. This was done in the framework of the time-dependent superfluid local density approximation (TDSLDA) or equivalently time-dependent density functional theory extended to superfluid systems. Since the first study concerning 240Pu, TDSLDA has been applied extensively to compound systems 236U, 240Pu, and 252Cf (spontaneous fission), and recently to odd systems 239U, 241Pu, and 238Np. During this talk I will summarize the results of such investigations, covering the following topics: the role of pairing correlations during fission, the properties of the FF spins and their correlations, complexity and entanglement, the dynamics of the neck rupture and emission of scission neutrons, the differences between odd and even-even fission dynamics, and the energy dependence of fission observables.