Additive manufacturing (AM) is a process in which parts are built up layer by layer, introducing novel approaches to how parts can be manufactured with less material waste, shorter lead times and lower costs than traditional manufacturing. One of the key advantages of AM over conventional manufacturing is its design flexibility, which enables for manufacturing of parts with highly detailed geometries in one go, leaving out the need for molding, casting, etc. However, due to the chamber size of the machines, the size of AM parts is limited. To overcome this limitation, joining AM parts together or to wrought or cast material has been proposed. Among the various welding technologies, laser welding is considered a suitable candidate for joining AM parts because of its low heat input, resulting in low deformation, high welding speed, and full automation capability. This study will provide a fundamental understanding of laser welding of AM parts by reviewing current research in the field. The possibility of joining most commonly used AM parts such as AlSi10Mg, AISI 316L, Ti6Al4V and Nickel alloy 718 by laser welding are investigated. Furthermore, the effect of laser welding parameters on mechanical and microstructural properties of joined AM parts are discussed.