  A detailed review of the literature for the last 5-10 years on epitaxial
growth of graphene is presented. Both experimental and theoretical aspects
related to growth on transition metals and on silicon carbide are thoroughly
reviewed. Thermodynamic and kinetic aspects of growth on all these materials,
where possible, are discussed. To make this text useful for a wider audience, a
range of important experimental techniques that have been used over the last
decade to grow (e.g. CVD, TPG and segregation) and characterize (STM, LEEM,
etc.) graphene are reviewed, and a critical survey of the most important
theoretical techniques is given. Finally, we critically discuss various
unsolved problems related to growth and its mechanism which we believe require
proper attention in future research.
