With the rapid development of on-chip optical interconnects and optical computing in the past decade, silicon-based integrated devices for monolithic and hybrid optoelectronic integration have attracted wide attention. Due to its narrow pseudo-direct gap behavior and compatibility with Si technology, epitaxial Ge-on-Si has become a significant material for optoelectronic device applications. In this paper, we describe recent research progress on heteroepitaxy of Ge flat films and self-assembled Ge quantum dots on Si. For film growth, methods of strain modification and lattice mismatch relief are summarized, while for dot growth, key process parameters and their effects on the dot density, dot morphology and dot position are reviewed. The results indicate that epitaxial Ge-on-Si materials will play a bigger role in silicon photonics.