We study theoretically the spectral and polarization threshold characteristics of Vertical-Cavity Surface-Emitting Lasers with nematic and cholesteric liquid crystal overlay: LC-VCSELs. In the first case, we demonstrate the possibility of selecting between two orthogonal directions of linear polarization (LP) of the fundamental mode (x or y LP) by choosing appropriate NLC length and to achieve strong polarization discrimination: threshold gain difference as large as several times the threshold gain. We also demonstrate an active control of light polarization by electro-optically tuning the LC director and show that either polarization switching between x and y LP modes or continuous change of the LP direction is possible. For cholesteric LC-VCSEL we show that it becomes a coupled system with different spectral, threshold and polarization characteristics than the ones of the stand-alone VCSEL. Due to the existence of a band gap for circularly polarized light in the liquid crystal, lasing occurs in almost circularly polarized modes at the LC side.