Construction of two-dimensional (2D) molecular crystals on solid surfaces is an important way to synthesize supermolecular materials and functionalize solid surfaces. In this review, we provide an overview of the formation mechanism of the 2D self-assembled molecular crystals, and the control of the structures and electronic structures by combining theoretical calculations with scanning tunneling microscopy (STM). Here we focus on the molecular selfassembled structures dominated by weak interactions. Several key factors are listed, for example, the electronic structures of solid surfaces, the configuration of molecules, the interaction of molecules, the interaction between molecules and substrates, and the bromine adatom assisted self-assembly. Finally, we assess future directions of research in this field, where the overall consideration of all the aspects we discussed is important.