Recent advances in additive manufacturing (AM) have attracted significant industrial interest. Initially, AM was mainly associated with the fabrication of prototypes, but the AM advances together with the broadening range of available materials, especially for producing metallic parts, have broaden the application areas and now the technology can be used for manufacturing functional parts, too. Especially, the AM technologies enable the creation of complex and topologically optimised geometries with internal cavities that were impossible to produce with traditional manufacturing processes. However, the tight geometrical tolerances along with the strict surface integrity requirements in aerospace, biomedical and automotive industries are not achievable in most cases with standalone AM technologies. Therefore, AM parts need extensive post-processing to ensure that their surface and dimensional requirements together with their respective mechanical properties are met. In this context, it is not surprising that the integration of AM with post-processing technologies into single and multi set-up processing solutions, commonly referred to as hybrid AM, has emerged as a very attractive proposition for industry while attracting a significant R&D interest. This paper reviews the current research and technology advances associated with the hybrid AM solutions. The special focus is on hybrid AM solutions that combine the capabilities of laser-based AM for processing powders with the necessary post-process technologies for producing metal parts with required accuracy, surface integrity and material properties. Commercially available hybrid AM systems that integrate laser-based AM with post-processing technologies are also reviewed together with their key application areas. Finally, the main challenges and open issues in broadening the industrial use of hybrid AM solutions are discussed.