With its outstanding physical properties, single crystal diamond is the material of choice for future power electronics and quantum devices. The later application field is based on the optical and spin properties of color centers hosted in diamond lattice. Two synthesis methods are currently developed to grow high quality diamond: high pressure and high temperature (HPHT) synthesis and chemical vapor deposition (CVD). This review describes the state of the art of single crystal diamond growth by CVD, either starting with diamond substrate (homoepitaxy) or controlling diamond epitaxial nucleation on a foreign substrate (heteroepitaxy). Progress on substrates, dislocation propagation and reduction of structural defects, doping, upscaling and applications are reviewed. In light of recent progress, future challenges and the respective roles of homoepitaxial and heteroepitaxial materials in the applications roadmap are discussed.