As an emerging class of new materials, two-dimensional (2D) non-graphene materials, including layered and non-layered, and their heterostructures are currently attracting increasing interest due to their promising applications in electronics, optoelectronics and clean energy. In contrast to traditional semiconductors, such as Si, Ge and III-V group materials, 2D materials show significant merits of ultrathin thickness, very high surface-to-volume ratio, and high compatibility with flexible devices. Owing to these unique properties, while scaling down to ultrathin thickness, devices based on these materials as well as artificially synthetic heterostructures exhibit novel and surprising functions and performances. In this review, we aim to provide a summary on the state-of-the-art research activities on 2D non-graphene materials. The scope of the review will cover the preparation of layered and non-layered 2D materials, construction of 2D vertical van der Waals and lateral ultrathin heterostructures, and especially focus on the applications in electronics, optoelectronics and clean energy. Moreover, the review is concluded with some perspectives on the future developments in this field.