Electrospinning has recently been developed as an efficient technique to develop polymeric nanofibres. Various synthetic and natural biodegradable polymers have been electrospun into fibres with diameters in the nanometre range (< 1 microm). The fibre diameter, structure and physical properties of the nanofibre matrices can be effectively tuned by controlling various parameters that affect the electrospinning process. The dimension and structure of electrospun polymeric nanofibre mats resembles mostly the collagen phase of natural extracellular matrix. This, combined with excellent physical properties such as high surface area, high porosity, interconnective pores of the nanofibre matrices and appropriate mechanical properties, well-controlled degradation rates and biocompatibility of the base polymer, make biodegradable polymeric nanofibre matrices ideal candidates for developing scaffolds for tissue engineering. This article reviews the recent advances in the development of synthetic biodegradable nanofibre-based matrices as scaffolds for tissue engineering.