Neutron scattering is proved to be a vital probe in unveiling the magnetic properties of high temperature superconductors (HTSC). Detailed information about the energy and momentum dependence of the magnetic dynamics of HTSC have been obtained directly by this technique. Over the past decade by improving the crystal growth methods, large and high quality single crystals of HTSC, which are essential for a neutron scattering experiment, have become available. The results of neutron scattering measurements on such crystals have considerably enhanced our understanding of the magnetism in HTSC both in the superconducting (SC) and normal states. In this review, the neutron scattering results on two main HTSC families, La2-xSrxCuO4 (LSCOx) and YBa2CuO3O6+x (YBCO6+x), are considered with an emphasis on the most prominent properties of these materials that are now widely accepted. These include the presence of strong antiferromagnetic (AF) fluctuations even in optimally doped region of the phase diagram, neutron resonance peak that scales with SC transition temperature, Tc, incommensurate magnetic fluctuations (stripes), and a pseudogap in the normal state of underdoped materials.