We discuss some generic features of the degenerate Fermi gases and draw several model-independent conclusions for such systems. Specifically, we show that a class of physical observables can be expressed in terms of one universal function, which is valid irrespective of the details of the microscopic state of the system, provided that certain very general conditions are met. In the course of discussion, we also mention the necessary modifications to the naive crossover model and possibly some new features brought about by the Feshbach resonance.