Compared to other welding processes, laser welding of sheet steels coated with various zinc- rich layers (galvanized, electrogalvanized, galvannealed, etc.) can permit weight reduction of automobiles plus increase in productivity. Some instances of laser welding of such coated steels have been reported. However, wider applications of lasers for this purpose are hampered by the low boiling temperature of zinc compared to the melting temperature of steel. During laser welding in the lap-joint configuration, the presence of vaporized zinc between the steel sheets often leads to expulsion of the weld metal or considerably weld porosity. Attempts to overcome this problem using Nd:YAG laser welding are reviewed. For the lap-joint configuration, techniques examined include provision of a gap between the sheets, use of geometrical solutions such as concave or convex surfaces, and pulsing or modulating the laser waveform. The effects on weld quality of power density, pulse time and pulse shaping (for pulsed welding), the coating type and weight, the location of the beam axis and beam focus with respect to the sheet surface(s) and the joint geometry (lap and edge) have been examined. The results provide insight into the weldability of coated sheet steels by the laser welding process as well as better assessment of viable approaches to this problem.