Phase contrast magnetic resonance angiography (PCMRA) is a non-invasive imaging modality that is capable of producing quantitative vascular flow velocity information. The encoding of velocity information can significantly increase the imaging acquisition and reconstruction durations associated with this technique. The purpose of this work is to provide mechanisms for reducing the scan time of a 3D phase contrast exam, so that hemodynamic velocity data may be acquired robustly and with a high sensitivity. The methods developed in this work focus on the reduction of scan duration and reconstruction computation of a neurovascular PCMRA exam. The reductions in scan duration are made through a combination of advances in imaging and velocity encoding methods. The imaging improvements are explored using rapid 3D imaging techniques such as spiral projection imaging (SPI), Fermat looped orthogonally encoded trajectories (FLORET), stack of spirals and stack of cones trajectories. Scan durations are also shortened through the use and development of a novel parallel imaging technique called Pretty Easy Parallel Imaging (PEPI). Improvements in the computational efficiency of PEPI and in general MRI reconstruction are made in the area of sample density estimation and correction of 3D trajectories. A new method of velocity encoding is demonstrated to provide more efficient signal to noise ratio (SNR) gains than current state of the art methods. The proposed velocity encoding achieves improved SNR through the use of high gradient moments and by resolving phase aliasing through the use measurement geometry and non-linear constraints.