High power laser welding in greater thickness offers many advantages in comparison with traditional welding processes. The advantages include low distortion, high productivity and low filler metal consumption. The introduction of the process in the welding industry does however involve a number of serious challenges caused by the nature of the process itself, and these challenges also differ from one base material to another. Techniques for optimisation of the weld quality are discussed and especially structural steels and the control of solidification flaw formation are dealt with. Today laser welding has reached a stage were, it has been introduced in e.g. European ship building. Very thick part CO2-laser welding using penetration depth in excess of approximately 15 mm in mild steel does however continue to be a serious challenge. This is due to limitations in the achievable welding depth because the penetration as a function of laser power shows a very unlinear behaviour. Possible causes are discussed and a simple mathematical model for the penetration as a function of laser power and welding speed is presented. The model is shown to be in fair agreement with the experimental observations.