Graphene, an atomic monolayer of carbon atoms in a honeycomb lattice realized in 2004, has rapidly risen as the hottest star in materials science due to its exceptional properties. The explosive studies on graphene have sparked new interests towards graphene-analogous materials. Now many graphene-analogous materials have been fabricated from a large variety of layer and non-layer materials. Also, many graphene-analogous materials have been designed from the computational side. Though overshadowed by the rising graphene to some degree, graphene-analogous materials have exceptional properties associated with low dimensionality and edge states, and bring new breakthrough to nanomaterials science as well. In this review, we summarize the recent progress on graphene-analogous low-dimensional materials (2D nanosheets and 1D nanoribbons) from both experimental and computational side, and emphasis is placed on structure, properties, preparation, and potential applications of graphene-analogous materials as well as the comparison with graphene. The reviewed materials include strictly graphene-like planar materials (experimentally available h-BN, silicene, and BC3 as well as computationally predicted SiC, SiC2, B, and B2C), non-planar materials (metal dichalcogenides, metal oxides and hydroxides, graphitic-phase of ZnO, MXene), metal coordination polymers, and organic covalent polymers. This comprehensive review might provide a directional guide for the bright future of this emerging area.