Synthetic polymer and biopolymer nanofibres can be fabricated through self-assembly, phase separation, electrospinning, and mechanical methods. These novel functional biocompatible polymers are very promising for a variety of future biomedical applications. There are many characteristics of nanofibres that would potentially influence cell growth and proliferation. As such, many studies have been carried out to elucidate the cell–nanofibre interaction with the purpose of optimizing the matrix for cell growth and tissue regeneration. In this Review, we present current literatures and our research on the interactions between cells and nanofibres, and the potentials of nanofibre scaffolds for biomedical applications.