The goal of this thesis is to develop advanced laser cutting techniques based on experimental and theoretical treatment of laser-material interactions, assist-gas flow and combustion reactions;A two-dimensional, conductive heat transfer model based on a moving line heat-source model was investigated in combustion-assisted laser cutting of mild steel. Laser characteristics (power, absorptivity, mode), combustion reaction (combustion heat, efficiency), and material properties (thermal properties, density, thickness and melt film thickness) were correlated to accurately predict the maximum cutting speed and kerf width;Advanced laser cutting techniques which employ the dual gas-jets or the axicon-lens doublet were investigated. Compared with the conventional laser cutting technique, these innovative methods significantly improve the cutting thickness, surface finish and productivity of difficult-to-machine materials such as stainless steels, superalloys, metal matrix composites, and ceramics. The effectiveness of the dual gas-jet laser cutting technique was attributed to the oxygen gas momentum transfer from the off-axial gas-jet, which reduced the concentration of passive oxides and consequently the viscosity and the solidification temperature of the melt. The off-axial gas-jet also provided a dynamic force to remove the melt/slag more efficiently. Analytical models based on fluid-dynamics and gas momentum transfer were developed to predict the cutting speeds in coaxial and dual gas-jet assisted laser cutting of mild and stainless steels. Laser cutting using axicon-lens doublet optics showed that the cutting time on chick eggs was shortened by five times when compared to the propane torch cutting method. A simple energy balance model based on the cutting mechanisms (vaporization and decomposition of egg shell) was used to predict the cutting and drilling time and the results agreed well with the experimental data;The standard laser cutting of polymers is often accompanied by charring and material degradation at the cut edges. A new experimental approach utilizing SF[subscript]6 plasma for effective polishing of cut surface during laser cutting of polymers was investigated. The plasma formation through the absorption of laser energy and dissociation of SF[subscript]6 and its effects on the surface finish of thermoplastic polymers including polyvinylchloride, polyamide, polypropylene and polyethylene were presented and discussed. (Abstract shortened with permission of author.)