Hybrid manufacturing (HM) integrates two or more distinct manufacturing processes—most commonly additive manufacturing (AM) and subtractive machining—within a coordinated workflow (often on a single platform) to achieve capabilities that neither process provides alone: high geometric freedom and rapid material addition from AM, plus tolerance, surface finish, and datum control from machining. This review first surveys major classes of hybrid manufacturing (additive–subtractive, multi-energy, multi-material, and assistive hybrid). It then focuses on multi-axis directed energy deposition (DED) combined with in-loop subtractive machining—arguably the most mature and industrially impactful HM configuration—emphasizing process planning methods, persistent limitations, and application domains, including repair/remanufacturing and functionally graded materials (FGMs). The review highlights current CAM strategies for hybrid DED, integrated planning frameworks, and emerging trends such as digital twins and closed-loop metrology-driven replanning.