Electrospun membranes are used in a variety of applications, including filtration systems and sensors for chemical detection, and have attracted increased interest in the field of tissue engineering and regenerative medicine. Successful integration of these materials into a specific technology will require understanding of the fibres' surface, bulk and architectural properties. Detailed characterisation of these properties is frequently overlooked, particularly in specialised interdisciplinary fields such as tissue engineering. In this article we have reviewed the current status of the characterisation of electrospun membranes, while recommending improvements in using these techniques to better understand these very interesting nanostructured materials.