The development of neovasculature via angiogenesis is a vital component of many normal physiological processes and a number of disease states. Neovascularisation is critical for the growth of malignant tumours and for the development and survival of metastases. Recently, the potential of non-invasive imaging for the functional characterisation of neovasculature has become realised. In this review we describe the process of tumour angiogenesis for radiologists and present a summary of the most available computed tomography/magnetic resonance imaging techniques that can depict the functional vascular status of human tumours.