The recent surge in graphene research has stimulated interest in the investigation of various 2-dimensional (2D) nanomaterials. Among these materials, the 2D boron nitride (BN) nanostructures are in a unique position. This is because they are the isoelectric analogs to graphene structures and share very similar structural characteristics and many physical properties except for the large band gap. The main forms of the 2D BN nanostructures include nanosheets (BNNSs), nanoribbons (BNNRs), and nanomeshes (BNNMs). BNNRs are essentially BNNSs with narrow widths in which the edge effects become significant; BNNMs are also variations of BNNSs, which are supported on certain metal substrates where strong interactions and the lattice mismatch between the substrate and the nanosheet result in periodic shallow regions on the nanosheet surface. Recently, the hybrids of 2D BN nanostructures with graphene, in the form of either in-plane hybrids or inter-plane heterolayers, have also drawn much attention. In particular, the BNNS-graphene heterolayer architectures are finding important electronic applications as BNNSs may serve as excellent dielectric substrates or separation layers for graphene electronic devices. In this article, we first discuss the structural basics, spectroscopic signatures, and physical properties of the 2D BN nanostructures. Then, various top-down and bottom-up preparation methodologies are reviewed in detail. Several sections are dedicated to the preparation of BNNRs, BNNMs, and BNNS-graphene hybrids, respectively. Following some more discussions on the applications of these unique materials, the article is concluded with a summary and perspectives of this exciting new field.