In biotechnology, the field of cell cultivation is highly relevant. Cultivated cells can be used, for example, for the development of biopharmaceuticals and in tissue engineering. Commonly, mammalian cells are grown in bioreactors, T-flasks, well plates, etc., without a specific substrate. Nanofibrous mats, however, have been reported to promote cell growth, adhesion, and proliferation. Here, we give an overview of the different attempts at cultivating mammalian cells on electrospun nanofiber mats for biotechnological and biomedical purposes. Starting with a brief overview of the different electrospinning methods, resulting in random or defined fiber orientations in the nanofiber mats, we describe the typical materials used in cell growth applications in biotechnology and tissue engineering. The influence of using different surface morphologies and polymers or polymer blends on the possible application of such nanofiber mats for tissue engineering and other biotechnological applications is discussed. Polymer blends, in particular, can often be used to reach the required combination of mechanical and biological properties, making such nanofiber mats highly suitable for tissue engineering and other biotechnological or biomedical cell growth applications.