The synthesis and structures of graphene on Ru(0001) and Pt(111), silicene on Ag(111) and Ir(111) and the honeycomb hafnium lattice on Ir(111) are reviewed. Epitaxy on a transition metal (TM) substrate is a promising method to produce a variety of two dimensional (2D) atomic crystals which potentially can be used in next generation electronic devices. This method is particularly valuable in the case of producing 2D materials that do not exist in 3D forms, for instance, silicene. Based on the intensive investigations of epitaxial graphene on TM in recent years, it is known that the quality of graphene is affected by many factors, including the interaction between the 2D material overlayer and the substrate, the lattice mismatch, the nucleation density at the early stage of growth. It is found that these factors also apply to many other epitaxial 2D crystals on TM. The knowledge from the reviewed systems will shine light on the design and synthesis of new 2D crystals with novel properties.