Over the past decade, graphene has advanced rapidly as one of the most promising materials changing human life. Development of production-worthy synthetic methodologies for the preparation of various types of graphene forms the basis for its investigation and applications. Graphene can be used in the forms of either microflake powders or large-area thin films. Graphene powders are prepared by the exfoliation of graphite or the reduction of graphene oxide, while graphene films are prepared predominantly by chemical vapor deposition (CVD) on a variety of substrates. Both metal and dielectric substrates have been explored; while dielectric substrates are preferred over any other substrate, much higher quality graphene large-area films have been grown on metal substrates such as Cu. The focus here is on the progress of graphene synthesis on Cu foils by CVD, including various CVD techniques, graphene growth mechanisms and kinetics, strategies for synthesizing large-area graphene single crystals, graphene transfer techniques, and, finally, challenges and prospects are discussed.