Two-dimensional (2D) materials have a unique crystal structure and excellent properties, which renders it possible to be used to construct novel artificial nanostructures and design novel nanodevices, thereby achieving a breakthrough in the semiconductor field. In this review paper, the basic behaviors of the ambipolar 2D crystals and the fabrication method of the van der Waals heterostructures are first introduced. We mainly summarize the applications of the ambipolar 2D crystals for novel electrical-field-tunable 2D p-n junctions and p-n heterojunctions (field-effect p-n heterojunction transistor) and non-volatile storable p-n junctions, and other aspects of the relevant structural design, electronic and optoelectronic properties. Then we further introduce their potential applications of logic rectifiers, field-effect optoelectronic transistors, multi-mode non-volatile memories, rectifier memories, optoelectronic memories, photovoltaics, etc. Finally, we provide an outlook of the future possible studies of this new type of p-n junctions in the relevant fields.