This review concentrates on the applications of nanoimprint lithography (NIL) and hot embossing for the fabrications of nanolectronic devices, nanophotonic metamaterials and other nanostructures. Technical challenges and solutions in NIL such as nanofabrication of templates, removal of residual resist, pattern displacement in thermal NIL arising from thermal expansion are first discussed. In the nanofabrication of templates, dry etch in plasma for the formation of multi-step structures and ultra-sharp tip arrays in silicon, nanophotonic chiral structures with high aspect ratio in SiC are demonstrated. A bilayer technique for nondestructive removal of residual resist in thermal NIL is described. This process is successfully applied for the fabrication of T-shape gates and functional high electron mobility transistors. However, pattern displacement intrinsically existing in thermal NIL/hot embossing owing to different thermal expansions in the template and substrate, respectively, limits its further development and scale-up. Low temperature even room temperature NIL (RTNIL) was then proposed on HSQ, trying to eliminate the pattern distortion by avoiding a thermal loop in the imprint. But, considerable pressure needed in RTNIL turned the major attentions to the development of UVcuring NIL in UV-curable monomers at low temperature. A big variety of applications by low-temperature UV-curing NIL in SU-8 are described, including high-aspect-ratio phase gratings, tagging technology by nanobarcode for DNA sequencing, nanofluidic channels, nanophotonic metamaterials and biosensors. Hot embossing, as a parallel technique to NIL, was also developed, and its applications on ferroelectric polymers as well as metals are reviewed. Therefore, it is necessary to emphasize that this review is mainly attempted to review the applications of NIL/embossing instead of NIL technique advances.