In non-central relativistic heavy-ion collisions, the large initial orbital angular momentum results in strong vorticity fields in the quark-gluon plasma, which polarize partons through the spin-orbit coupling. The global polarization of quark matter will be converted to the global polarization of baryons and the global spin alignment of vector mesons. The spin alignment refers to the $\rho_{00}$ element of the spin density matrix for vector mesons. When a vector meson decays to two pseudoscalar mesons, the polar angle distribution for the decay product depends on $\rho_{00}$ , through which the spin alignment can be measured. Theoretical studies show that the global spin polarization of baryons reflects the space-time average of the quark polarization, while the spin alignment of vector mesons reflects the local phase space correlation between the polarization of quark and antiquark. In this article, we review recent theoretical works about the spin alignment of vector mesons. We consider a non-relativistic quark coalescence model in spin and phase space. Within this model, the spin alignment of the vector meson can be described through the phase space correlation of quark's and antiquark's polarization. The contributions to the spin alignment of ϕmesons from vorticity fields, electromagnetic fields, and effective ϕmeson fields are discussed. The spin alignment of vector mesons opens a new window for the properties of strong interaction fields in heavy-ion collisions.