Cultivated meat (CM) technology has the potential to disrupt the food industry—indeed, it is already an inevitable reality. This new technology is an alternative to solve the environmental, health and ethical issues associated with the demand for meat products. The global market longs for biotechnological improvements for the CM production chain. CM, also known as cultured, cell-based, lab-grown, in vitro or clean meat, is obtained through cellular agriculture, which is based on applying tissue engineering principles. In practice, it is first necessary to choose the best cell source and type, and then to furnish the necessary nutrients, growth factors and signalling molecules via cultivation media. This procedure occurs in a controlled environment that provides the surfaces necessary for anchor-dependent cells and offers microcarriers and scaffolds that favour the three-dimensional (3D) organisation of multiple cell types. In this review, we discuss relevant information to CM production, including the cultivation process, cell sources, medium requirements, the main obstacles to CM production (consumer acceptance, scalability, safety and reproducibility), the technological aspects of 3D models (biomaterials, microcarriers and scaffolds) and assembly methods (cell layering, spinning and 3D bioprinting). We also provide an outlook on the global CM market. Our review brings a broad overview of the CM field, providing an update for everyone interested in the topic, which is especially important because CM is a multidisciplinary technology.