This paper presents a review of diverse superfluid pairing mechanisms and their associated many-body states in polarized Fermi gases. Based on the Bardeen-Cooper-Schrieffer theory, we analyze the role of Fermi surface properties in governing atomic pairing behavior, and subsequently introduce the finite-momentum pairing mechanism. Then we examine how spin-orbit coupling, serving as an artificial gauge field, modulates these finite-momentum pairing states. Furthermore, we focus on the altermagnetic state, which is characterized by broken time-reversal symmetry and vanishing net magnetization. We discuss that its alternating polarization in the momentum space can lead to the Fermi surface anisotropy that generates unconventional pairing associated with the spatial point-group symmetry. Finally, we discuss the polaron with the quasiparticle behavior manifested by minority impurity atoms in the extreme polarization limit, and explore its applications in probing many-body physics. The above investigations reveal the rich phase diagram of polarized Fermi gases spanning from collective pairing to single-impurity excitations, and lay the theoretical and experimental groundwork for the exploration of novel quantum many-body states.