Hexagonal boron nitride (h-BN) is structurally like graphite and has continued to gain research interest from synthesis, characterization, to application. Mono and few layered h-BN are now commonly known as boron nitride nanosheets (BNNSs), as one of the emerging two-dimensional (2D) materials. On the other hand, seamless rolls of BNNSs are known as boron nitride nanotubes (BNNTs). BNNTs are meaningful as a role model of materials by design, as they are first predicted by theory and then experimentally realized. Due to the difficulty on the synthesis of BNNTs and BNNSs, their research progress is far slower than the structurally similar carbon nanotubes (CNTs) and graphene. In this invited talk, recent advancement of BNNTs and BNNSs will be discussed, in particular for their application in advanced electronic and biomedical applications. These advancements suggest that BNNTs and BNNSs are important nanomaterials that complement the application of CNTs, graphene, and 2D materials.