The implementation of additive manufacturing for ceramics is more challenging than for other material classes, since most of the shaping methods require polymer binder. Laser additive manufacturing (LAM) could offer a new binder-free consolidation route, since it is capable of processing ceramics in a direct manner without post-processing. However, laser processing of ceramics, especially high performance oxide ceramics, is limited by low thermal shock resistance, weak densification and low light absorptance at room temperature; particularly in the visible or near-infrared range. An extensive review focusing only on LAM (powder bed fusion - laser beam and directed energy deposition) of high performance oxide ceramics is currently lacking. This state-of-the-art review gives a detailed summary and critical analysis about process technologies, part properties, open challenges and process monitoring in the field of oxide ceramics. Improvements in accuracy and mechanical strength are proposed that could open LAM of oxide ceramics to new fields.