Global pressure from consumers to improve animal welfare, and reduce microbiological risks or the use of antibiotics pose new challenges for the meat industry. Today's livestock production, despite many undertaken measures, is still far from being sustainable. This forced the need to work on alternative protein types that come from plants, insects, fungi, or cell culture processes. Due to some technical and legal barriers, cultivated meat is not present on the European market, however, in 2020 it was approved in Singapore and in 2022 in the USA. While the technology of obtaining cell cultures from animal muscles has been known and successfully practiced for years, the production of a stable piece of meat with appropriate texture, taste, and smell, is still a problem for several scientific groups related to subsequent companies trying to obtain the highest quality product, in line with the expectations of customers. Although the work on optimal cell meat production has been going on for years, it is still in an early stage, mainly due to several limitations that represent milestones for industrial production. The most important are: the culture media (without animal serum), which will provide an environment for optimal muscle development, natural or close to natural (but still safe for the consumer) stable scaffolds for growing cells. Here, we review the actual knowledge about the above-mentioned challenges which make the production of cellular meat not yet developed on an industrial scale.