Abstract: Extensive studies of low-dimensional carbon nanomaterials have attracted tremendens attention to the allotropes of other elements. Boron nitride nanomaterials are structurally analogous to carbon nanomaterials, but possess quite different properties. Unlike metallic or semiconducting carbon nanotubes (CNTs), the boron nitride nanotubes (BNNTs) are electrical insulators, basically independent of their diameters and chirality. BNNTs possess high thermal conductivity, excellent mechanical properties, and high chemical stability. The same advantages are applicable to two-dimensional monolayer boron nitride sheets. These unique properties make BNNTs and BN sheets promising nanomaterials in many potential fields, such as optoelectronic nanodevices, functional composites, hydrogen storage, and catalyze. This paper reviewed our theoretical studies on the BNNTs and BN sheets, including their electronic properties, chemical modification, defects, hydrogen storage and boron nitride super-architecture.