A literature review is made on the numerical models of wave-induced currents. The major processes of the flow system are wave breaking, bottom friction of combined wave-current flow and mixing processes primarily caused by wave breaking as well as the flow fields of waves and currents themselves. The survey is given to each item with great emphasis on numerical implication as well as physical mechanism. As noted is the importance in recent investigations, a brief treatment is also given on the currents driven by random or spectral waves.