Cultivated meat (clean meat) is an emerging yet fast growing research field and industry with a great potential to overcome the limitations of traditional cattle meat production. Cultivated meat leverages the technologies of cell biology and tissue engineering, culturing multiple types of cells and assembling them into a tissue structure construct mimicking the muscle tissues of livestock animals. A sustainable cell source is the first and the utmost important component of cultivated meat technology. In this mini review, cell sources for the main cell types in cultivated meat (muscle cells and fat cells) are described. Stem cells with self-renewal and differentiation potential are the most prominent candidates. Progenitor stem cells from muscle tissues, mesenchymal stem cells isolated from many other tissues and induced Pluripotent Stem Cells (iPSCs) created from terminally differentiated cells have been used as cell sources for cultivated meat. To become a sustainable cell source, which can generate high quantity (extensive in vitro expansion) and high quality (stemness) cells for the making of cultivated meat, these cells still face the challenges and limitation intrinsically associated with in vitro culturing. The efforts and strategies to circumvent such limitations are also discussed.