Two-dimensional (2D) materials have received extensive research attentions over the past two decades due to their intriguing physical properties (such as the ultrahigh mobility and strong light-matter interaction at atomic thickness) and a broad range of potential applications (especially in the fields of electronics and optoelectronics). The growth of single-crystal 2D materials is the prerequisite to realize 2D-based high-performance applications. In this review, we aim to provide an in-depth analysis of the state-of-the-art technology for the growth and applications of 2D materials, with particular emphasis on single crystals. We first summarize the major growth strategies for monolayer 2D single crystals. Following that, we discuss the growth of multilayer single crystals, including the control of thickness, stacking sequence, and heterostructure composition. Then we highlight the exploration of 2D single crystals in electronic and optoelectronic devices. Finally, a perspective is given to outline the research opportunities and the remaining challenges in this field.