A phase-only hologram (POH) has two major advantages. First, it can be displayed with a single phase-only SLM. Second, the reconstructed image is brighter, and free from the zeroth-order diffraction and the twin image. In this paper, four modern methods for the generation of POH, are reviewed. Being different from some existing approach that involved multiple epochs of evaluation in the generation of POH, the methods describe in this paper are non-iterative and computationally efficient. Moreover, these works also share the common feature that the holograms generated can be displayed directly on the phase-only SLM, hence simplifying the optical setup.