Abstract With the introduction of fiber-guided radiation at 1 μ wavelength emitting in the milti-kW range at better beam quality than CO 2-lasers the most established application in laser processing, namely laser fusion cutting, came back into the industrial and scientific focus. Laser sources with extraordinary optical and economical properties — disk and fiber lasers — in a stormy way enter the market of cutting machines so far reserved for the 10 μ radiation source and led to a volatile situation. The new laser sources can already address a market-relevant class of applications, namely, fusion cutting of steel up to a sheet thickness of 2 mm with pronounced advantages in productivity. However, there is a significant lack of cut quality for larger sheet thickness. The main reason for the drawback and its physical background are given. With the availability of cutting machines with 1 μ fiber-guided radiation the race for the worldwide market regarding the larger sheet thickness is opened and the priority issues to improve the cut quality are related to the three levels: wavelength, beam delivery and the application stage of the machine. The stability model called QuCut is presented which for the first time allows to analyze stability of cutting with fiber-guided radiation. Experimental ripple patterns and ripple spectra resolved with respect to the cutting depth are well reproduced by the new stability model. A number of different experimental methods towards an improved understanding of the dynamics in laser drilling are developed, however, there are gaps related to in-situ observation which is obscured by the hole walls. There are four novel experimental methods resolving the dynamics from a μms-down to a n s -time scale having a spatial resolution with respect to transient drilling depth on the μm scale. As result, the different mechanisms contributing to recast formation and dynamical features of drilling are revealed in more detail. In particular, the action of double pulses and its changes depending on the evolving drill are investigated.