We review a few ideas and experiments that our laboratory at Korea University has proposed and carried out to use vector polarizability β to manipulate alkali-metal atoms. β comes from spin-orbit coupling, and it produces an ac Stark shift that resembles a Zeeman shift. When a circularly polarized laser field is properly detuned between the D 1 and D 2 transitions, an ac Stark shift of a ground-state atom takes the form of a pure Zeeman shift. We call it the "analogous Zeeman effect", and experimentally demonstrated an optical Stern-Gerlach effect and an optical trap that behaves exactly like a magnetic trap. By tuning polarization of a trapping beam, and thereby controlling a shift proportional to β, we demonstrated elimination of an inhomogeneous broadening of a ground hyperfine transition in an optical trap. We call it "magic polarization".We also showed significant narrowing of a Raman sideband transition at a specific well depth. A Raman sideband in an optical trap is broadened owing to anharmonicity of the trap potential, and the broadening can be eliminated by a β-induced differential ac Stark shift at what we call a "magic well depth". Finally, we proposed and experimentally demonstrated a cooling scheme that incorporated the idea of velocity-selective coherent population trapping to Raman sideband cooling to enhance cooling efficiency of the latter outside of the Lamb-Dicke regime. We call it "motionselective coherent population trapping", and β is responsible for the selectivity. We include as Supplementary Material a program file that calculates both scalar and vector polarizabilities of a given alkali-metal atom when the wavelength of an applied field is specified. It also calculates depth of a potential well and photon-scattering rate of a trapped atom in a specific ground state when power, minimum spot size, and polarization of a trap beam are given.