This thesis presents theoretical work in s- and p-wave resonantly paired Fermi gases at zero temperature. In the BEC regime of the wide-resonance s-wave BCS-BEC crossover, the chemical potential, speed of sound, condensate depletion, and ground state energy are computed. The quantities are calculated in a low density approximation. The bosonic scattering length is computed diagrammatically to be approximately 0.60a with a the fermionic scattering length, confirming a well-known result. The perturbative approach breaks down in the intermediate BCS-BEC crossover regime which is not investigated. Quantum corrections are computed in the low density expansion, and the mass-imbalanced two-species Fermi gas is investigated. For identical fermions, it is discussed how p-wave Feshbach resonances naturally fall into two classes of "weak" and "strong", depending on the short-distance physics. It is shown how bound fermionic trimers appear in the strongly-resonant superfluid. The appearance of the trimer under the strengthening of the resonance is investigated, and the lifetime of p-wave diatomic molecules due to collisional relaxation into trimers is estimated.