Graphene, as the representative of two-dimensional materials, has varous novel physical properties and potential applications. The intrinsic zero band gap of graphene limits its application in semiconductor devices, and thus the search for new semiconducting alternative materials has become a current research hotspot. Phosphorene is the monolayer of black phosphorus and has a puckered honeycomb structure. Its advanced properties, such as adjustable direct band gap, high carrier mobility and in-plane anisotropy and so on, have recently aroused great research interest, thus opening up the research field of puckered honeycomb monolayers in group V elements. In this article, we first focus on the structure, synthesis and physical properties of five single-element two-dimensional materials (nitrogen, phosphorus, arsenic, antimony and bismuth) each with puckered honeycomb structure. Second, some binary two-dimensional materials with puckered honeycomb structure are discussed, including IV-VI and V-V compounds. These materials have their own unique crystal symmetry, and the properties can be controlled by changing their structures and dimensions. Finally, we also make a summary on some current challenges that need to be solved, and the possible future applications of these two-dimensional materials are also presented.