I will provide an overview of low-rank time integrators for time-dependent PDEs, with a particular focus on kinetic models. These integrators include an explicit method involving time-stepping followed by an SVD truncation procedure, applied to the nonlinear Vlasov model, implicit integrators leveraging extended Krylov subspaces for the Fokker-Planck equation, and  implicit-explicit low-rank integrators for multi-scale linear transport equations. A key feature of our algorithm is its significantly reduced computational complexity, which scales linearly with the number of grid points per dimension and polynomially with respect to the rank. Additionally, we develop Locally Macroscopic Conservative (LoMaC) projections to preserve the underlying macroscopic structure of the kinetic system. A wide range of benchmark tests have been conducted to demonstrate the efficiency and effectiveness of the proposed scheme.