Boosted by the great success of graphene, the past decade has witnessed the rapid development of graphene-analogous two-dimensional (2D) nanomaterials. Despite the high similarity in their lattice structure, the uniqueness of their specific atomic arrangement gives rise to a vast diversity of properties and thus a wide range of applications. This article provides a comprehensive review of recent progress on the properties, modeling investigations and applications of graphene-analogous 2D nanomaterials. It begins with the introduction of mechanical, thermal, electronic, optical and catalytic properties of various graphene-analogous 2D nanomaterials in associated with their unique atomic structures. The main modeling techniques of ab initio calculation and molecular dynamics simulation for the theoretical study of graphene-analogous 2D nanomaterials are then introduced, followed by the detailed discussion on the critical findings for each material. Thereafter, various intriguing applications, particularly in electronics, energy storage, catalysts, sensors, thermoelectric, lubricant and seawater desalination are highlighted. Finally, this review concludes with a perspective in this promising field on the basis of its current development.