Laser fusion welding-brazing processes are methods to metallurgically join dissimilar alloys with different melting points by laser heating to melt materials (substrate and filler material) with lower melting point, and by the interaction between the weld pool and the solid substrate with higher melt point at the joint interface. Laser fusion welding-brazing processes of dissimilar alloys are classified according to the laser energy absorption mechanisms. The development and state of the art of laser fusion welding-brazing processes are reviewed.