Cultivated meat, along with plant-based and insect-based alternatives, as well as proteins and biomass derived from fermentation processes, is considered a potentially sustainable alternative to conventional meat production. This review provides an overview of the concept of cultivated meat production and explains what efforts are currently being made in research and development to establish it as a sustainable and healthy food. The focus is on the current (bio)technological challenges, especially in production. To produce a structured product that resembles animal tissue, the growth of cells on suitable edible and biocompatible scaffold matrices is a prerequisite. In addition to this approach, there are also non-scaffold based methods such as 3D-bioprinting. Regardless of the method chosen, however, scaling up the growth and differentiation processes is crucial to increase the efficiency of the entire process. This article provides an overview of the current state of the art and derives approaches for future research projects, taking sustainability aspects into account.