An overview of laser-assisted nanofabrication methods, which has been developed in the Laser Processing Laboratory, is presented. All methods imply the laser-related ablation of material from a solid target and the production of nanoparticles or nanostructures. We consider the nanofabrication process in both the gaseous and in the liquid ambience under different parameters of laser radiation. A particular attention is given on the absence or presence of the plasma-related absorption of the laser radiation, which make possible different nanofabrication regimes. The methods lead to a production of nanomaterials, which are of importance for photonics and biosensing applications.