Cultured Meat (CM) is a growing field in cellular agriculture, driven by the environmental impact of conventional meat production, which contributes to climate change and occupies ≈70% of arable land. As demand for meat alternatives rises, research in this area expands. CM production relies on tissue engineering techniques, where a limited number of animal cells are cultured in vitro and processed to create meat-like tissue comprising muscle and adipose components. Currently, CM is primarily produced on a small scale in pilot facilities. Producing a large cell mass based on suitable cell sources and bioreactors remains challenging. Advanced manufacturing methods and innovative materials are required to subsequently process this cell mass into CM products on a large scale. Consequently, CM is closely linked with biofabrication, a suite of technologies for precisely arranging cellular aggregates and cell-material composites to construct specific structures, often using robotics. This review provides insights into contemporary biomedical biofabrication technologies, focusing on significant advancements in muscle and adipose tissue biofabrication for CM production. Novel materials for biofabricating CM are also discussed, emphasizing their edibility and incorporation of healthful components. Finally, initial studies on biofabricated CM are examined, addressing current limitations and future challenges for large-scale production.