Non-linear processes in the extreme ultraviolet

Recent developments in extreme ultraviolet (XUV) and x-ray radiation sources have pushed pulse energies and durations to unprecedented levels that opened up the era of non-linear XUV and x-ray optics. In this quest, laser driven high order harmonic generation sources providing attosecond resolution in the XUV spectral region enabled XUV-pump-XUV-probe experiments, while Free Electron Laser research infrastructures offer unique x-ray brilliances for highly non-linear interactions and since recently, they too entered the sub-fs temporal regime. This topical review discusses the conceptual intricacies of non-linear XUV and x-ray processes, addresses experimental particularities and highlights recent applications of such processes with emphasis to laser driven XUV-attosecond source related research.