Basic mechanisms of laser interaction with synthetic diamond are reviewed. The features of the major regimes of diamond surface etching are considered. Besides well-known graphitization and ablation processes, the nanoablation and accumulative graphitization, which attracted the attention relatively recently, are described in detail. The focus is placed on femtosecond (fs) laser exposure which provides a formation of dense cold electron-hole plasma in focal zone and a minimum overheating in surrounding area. This potentially opens the way to develop unique laser-based technologies combining physical and chemical processes for precise surface treatment and functionalization. The physical limitations determining how precisely the diamond surface can be treated by short-pulsed laser radiation and possible pathways to overcome them with the end to remove ultra-thin layers of the material are discussed. Particular attention is devoted to the novel possibility to induce local formation of point active defects - nitrogen vacancy (NV) complexes in the laser-irradiated zone. Both the regimes of NV centers generation with and without graphitization of diamond lattice are reviewed. It is thus shown that intensive pulse laser radiation is a perfect tool for processing of synthetic diamonds on the micro, nano and even on an atomic level that can be well controlled and managed.