This review provides a comprehensive theoretical overview of ultracold atomic Fermi gases, focusing on the effects of interactions in both uniform and harmonically trapped systems. The authors emphasize the crucial role of interactions in bringing the gas into a superfluid phase at low temperatures. The $s$-wave scattering length, a single parameter characterizing the interactions, can be tuned using external magnetic fields near Feshbach resonances. Key regimes discussed include the BCS limit, Bose-Einstein condensation (BEC) of dimers, and the unitary limit. The review covers various physical properties such as density profiles, momentum distributions, collective oscillations, pair-breaking effects, and the expansion of the gas. Theoretical approaches range from mean-field descriptions to quantum Monte Carlo techniques, with a focus on comparing theoretical predictions with experimental results. The review also explores the dynamics of superfluidity, the behavior in optical lattices, and the signatures of superfluidity, such as quantized vortices and the quenching of the moment of inertia.This review provides a comprehensive theoretical overview of ultracold atomic Fermi gases, focusing on the effects of interactions in both uniform and harmonically trapped systems. The authors emphasize the crucial role of interactions in bringing the gas into a superfluid phase at low temperatures. The $s$-wave scattering length, a single parameter characterizing the interactions, can be tuned using external magnetic fields near Feshbach resonances. Key regimes discussed include the BCS limit, Bose-Einstein condensation (BEC) of dimers, and the unitary limit. The review covers various physical properties such as density profiles, momentum distributions, collective oscillations, pair-breaking effects, and the expansion of the gas. Theoretical approaches range from mean-field descriptions to quantum Monte Carlo techniques, with a focus on comparing theoretical predictions with experimental results. The review also explores the dynamics of superfluidity, the behavior in optical lattices, and the signatures of superfluidity, such as quantized vortices and the quenching of the moment of inertia.