There have been breakthroughs in the mass production of graphene by chemical vapor deposition (CVD) and its practical applications have also been identified. Grain boundaries are typically present in 'CVD graphene' and adversely impact its properties. We summarize recent progress in growing large-area single crystal graphene. Centimeter-scale single-crystal, truly single-layer graphene (SLG) films have been reportedly achieved on single-crystal Cu(111) foils by CVD growth, while meter-scale single-crystal SLG films have been reportedly produced with assistance of a roll-to-roll technique. The growth of uniform single crystals of bilayer or multilayer graphene over a large area remains an exciting challenge. Layer-by-layer transfer and the stacking of single-crystal SLG is considered a promising route to making new types of 'single' crystals or quasicrystals with specific numbers of layers and different stacking angles.