Advanced micro/nanofabrication of functional materials and structures with various dimensions represents a key research topic in modern nanoscience and technology and becomes critically important for numerous emerging technologies such as nanoelectronics, nanophotonics and micro/nanoelectromechanical systems. This review systematically explores the non-conventional material processing approaches in fabricating nanomaterials and micro/nanostructures of various dimensions which are challenging to be fabricated via conventional approaches. Research efforts are focused on laser-based techniques for the growth and fabrication of one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) nanomaterials and micro/nanostructures. The following research topics are covered, including: 1) laser-assisted chemical vapor deposition (CVD) for highly efficient growth and integration of 1D nanomaterial of carbon nanotubes (CNTs), 2) laser direct writing (LDW) of graphene ribbons under ambient conditions, and 3) LDW of 3D micro/nanostructures via additive and subtractive processes. Comparing with the conventional fabrication methods, the laser-based methods exhibit several unique advantages in the micro/nanofabrication of advanced functional materials and structures. For the 1D CNT growth, the laser-assisted CVD process can realize both rapid material synthesis and tight control of growth location and orientation of CNTs due to the highly intense energy delivery and laser-induced optical near-field effects. For the 2D graphene synthesis and patterning, room-temperature and open-air fabrication of large-scale graphene patterns on dielectric surface has been successfully realized by a LDW process. For the 3D micro/nanofabrication, the combination of additive two-photon polymerization (TPP) and subtractive multi-photon ablation (MPA) processes enables the fabrication of arbitrary complex 3D micro/nanostructures which are challenging for conventional fabrication methods. Considering the numerous unique advantages of laser-based techniques, the laser-based micro/nanofabrication is expected to play a more and more important role in the fabrication of advanced functional micro/nano-devices.