Neutrons play a crucial role in initiating and sustaining the fission reaction. When a neutron collides with a nucleus of a fissile material like Uranium-235 or Plutonium-239, it can cause the nucleus to become unstable and split. The fission of the nucleus releases additional neutrons, which can then catalyze further fission events in a chain reaction. This self-sustaining chain reaction is the principle behind both nuclear reactors and atomic bombs.