We examine nuclear scission within a fully quantum-mechanical microscopic framework, focusing on the nonlocal aspects of the theory. Using (240)Pu hot fission as an example, we discuss the identification of the fragments and the calculation of their kinetic, excitation, and interaction energies, through the localization of the orbital wave functions. We show that the disentanglement of the fragment wave functions is essential to the quantum-mechanical definition of scission and the calculation of physical observables. Finally, we discuss the fragments' prescission excitation mechanisms and give a nonadiabatic description of their evolution beyond scission.