Functional nanofibrous scaffolds produced by electrospinning have great potential in many biomedical applications, such as tissue engineering, wound dressing, enzyme immobilization and drug (gene) delivery. For a specific successful application, the chemical, physical and biological properties of electrospun scaffolds should be adjusted to match the environment by using a combination of multi-component compositions and fabrication techniques where electrospinning has often become a pivotal tool. The property of the nanofibrous scaffold can be further improved with innovative development in electrospinning processes, such as two-component electrospinning and in-situ mixing electrospinning. Post modifications of electrospun membranes also provide effective means to render the electrospun scaffolds with controlled anisotropy and porosity. In this article, we review the materials, techniques and post modification methods to functionalize electrospun nanofibrous scaffolds suitable for biomedical applications.