Sheet metals such as titanium alloys, steel alloys, and aluminum alloys are significant materials due to their importance among everyday life products as well as high-strength applications in aircraft, ships, automobiles, construction, military, and marine purposes. Recently, laser cutting is one of the best and fastest non-conventional methods to cut sheet metals, so it is necessary to understand how laser cutting parameters affect cutting quality. A comprehensive review was presented to investigate how laser cutting parameters affect the cut surface and kerf quality and which parameters affect cutting quality the most. An overview of the advantages of laser cutting when compared to other methods of machining was presented. In addition, a description of the laser cutting method and the different sources of laser were presented with clearing the range of thicknesses of the cut material for each source and their advantages. Also, a description of the properties and the applications of the studied materials were discussed. The performance parameters ofcutting were illustrated in detail by graphs and equations. The research analysis and discussion were discussed in such organized details by tables and graphs which show the full classification of the studied papers. It was found that the best conditions to obtain low surface roughness, small HAZ width, small kerf width, and small kerf angle are using low laser power, high cutting speed, medium gas pressure, high standoff distance, medium pulse frequency, medium pulse width, small nozzle diameter, small thickness, and nitrogen as an assist gas.