Subcriticality is an academic concept and research domain focusing on the state of a nuclear system characterized by an effective neutron multiplication factor less than one, where the fission chain reaction is not self-sustaining without an external neutron source. This field investigates the physics and behavior of such systems, including neutron transport, reaction kinetics, and inherent stability properties. Its significance encompasses ensuring nuclear safety in operations like fuel storage and transport, and enabling the design and analysis of advanced systems, such as Accelerator-Driven Systems, which leverage this state for enhanced safety and waste management applications.