Magnetic resonance angiography (MRA) permits the non-invasive visualization of blood flow through the effects of moving spins on the magnetic resonance signal. MRA techniques can be divided into two main classifications depending upon the primary effect responsible for contrast in the image. Angiograms can be produced using either the time-of-flight (TOF) or phase contrast (PC) methods. Each method has particular advantages and limitations as an angiographic imaging technique and these are reflected in their respective applications. This review article is intended to outline the scientific and technical development of MRA from its basis in the earliest in vitro nuclear magnetic resonance (NMR) experiments, through the implementation of in vivo angiographic techniques on whole body MRI systems, to the recent rapid expansion in MRA acquisition and processing techniques.