Chaotic synchronization of semiconductor lasers with the coupling and its application in optical logic gates are studied. The constructions of the fundamental all-optical and optoelectronic logic gates using two chaotic lasers due to the mutual coupling and their computational principle are presented theoretically. All-optical logic gates are finally performed by synchronizing or unsynchronizing appropriately the two chaotic states via modulating the coupling light. And the optoelectronic logic gate is implemented by synchronizing or unsynchronizing appropriately the two chaotic states via modulating the current and coupling light together. All-optical XNOR, NOR, NOT, optoelectronic logic gates and their logic computational methods are presented. Numerical simulative results validate the feasibility of the system.