Laser cutting is an attractive alternative to conventional cutting methods due to its many inherent advantages. However, notwithstanding its promise for processing diverse categories of materials, the understanding of the subject is incomplete. Although numerous processes are known to significantly influence cutting quality, comprehensive data of practical utility - such as identification of processing regimes to achieve optimum cut surface attributes - remain yet to be generated. The present article establishes a methodology to develop such "processing maps" and illustrates their utility by using laser cutting of mild steel and commercially pure titanium as case studies. The processing maps can be constructed based on any chosen cut quality criteria and can be used to optimize the process on the basis of operational costs. Results reveal that, for achieving good quality cuts, such processing regimes constitute only a narrow region within the wide operating window for mere cuttability and vary substantially with material-assist gas combination. Typically, the operating window for inert gas-assisted cutting is narrower than that for oxygen-assisted cutting involving an exothermic oxidation reaction, which contributes significantly to the overall energy input to the cutting front. The influence of the two major process parameters, laser power and cutting speed, on cut quality attributes such as surface roughness, kerf width, heat affected zone, and cut surface morphology is also discussed in detail. The experimental results have also been compared with theoretical predictions of a scaling law for laser cutting. © 1999 Laser Institute of America.