This chapter presents an overview of direct graphene growth on silicon (Si) and silicon carbide (SiC) substrates. It discusses the relevance and challenges of graphene growth on Si substrates. The chapter provides a comprehensive scientific progress of graphene growth on silicon carbide (SiC) to date and evaluate its future perspective. It also discusses the graphene growth from heteroepitaxial cubic silicon carbide (3C-SiC) on large-area Si substrates as the most promising method to achieve direct growth of graphene on silicon substrates. Carbon ion implantation is an alternative approach for obtaining graphene directly on a Si substrate. Molecular beam epitaxy (MBE) growth of graphene is an additional method emerging, together with carbon ion implantation. Thermal decomposition is the most widely investigated technique for obtaining epitaxial graphene on 3C-SiC on Si. The chapter focuses on the impact of graphene growth on Si and SiC in connection to future technology.