Pulsars are among the most mysterious astrophysical objects in the Universe and are believed to be rotating neutron stars formed in supernova explosions. They are unique testing grounds of dense matter theories and gravitational physics and also provide links among nuclear physics, particle physics and General Relativity. Neutron stars may exhibit some of the most extreme and exotic characteristics that could not be found elsewhere in the Universe. Their properties are largely determined by the equation of state (EOS) of neutron-rich matter, which is the chief ingredient in calculating neutron star structure and properties of related phenomena, such as gravitational wave emission from deformed pulsars. Presently, the EOS of neutron-rich matter is still very uncertain mainly due to the poorly known density dependence of the nuclear symmetry energy especially at supra-saturation densities. Nevertheless, significant progress has been made recently in constraining the density dependence of the nuclear symmetry energy mostly at sub-saturation densities using terrestrial nuclear reactions. While there are still some uncertainties especially at supra-saturation densities, these constraints could provide useful information on the limits of the global properties of pulsars and the gravitational waves to be expected from them. Here we review our recent work on constraining properties of pulsars and gravitational radiation with data from terrestrial nuclear laboratories.