There are no lasers operating in the extreme ultraviolet or x-ray spectral region. Here, the only possibility to obtain coherent radiation in a laboratory scale is frequency conversion from lasers operating at other wavelengths. These processes are in general very inefficient. Thus, it is advantageous to recycle the non-converted light in an enhancement cavity. This thesis is about the scaling of average power and intensity in ultrashort pulse enhancement cavities. Here, pulses from a modelocked laser are continuously coupled into an external optical resonator, allowing for a pulse energy enhancement of orders of magnitude. The main applications are on the one hand the generation of high harmonics of the near infrared light into the extreme ultraviolet spectral region, and on the other hand the generation of hard x-ray radiation via inverse Compton scattering (also known as Thomson scattering). For both applications intensities ranging from 10 13 −10 15 W/cm 2 with several kilowatt of average power are required. In this regime, avoiding damage of the cavity mirrors is difficult. To this end, the circulating beam must have a large cross section on all cavity optics. In this work, design criteria aiming at this are developed and its implementation, in particular regarding the misalignment sensitivity, is investigated and demonstrated. Furthermore, the optimization of the resonator's thermal properties is necessary for fulfilling the target parameters. Here, this is achieved both by proper choice of the cavity geometry, and by custom mirrors with reduced absorption and improved thermal deformation. This allowed for average powers of several 100s of kilowatts with ultrashort pulses. This power regime is in particular interesting for inverse Compton scattering. These finding were used for the enhancement of 30-fs pulses to 10 kW of average power. This allowed for the generation of high harmonics with photon energies exceeding 100 eV at 250 MHz repetition rate. In this experiment, for the first time the photon flux was sufficient for experiments aiming at the study of dynamics on surfaces using photo electron emission microscopy (PEEM). Danksagung Diese Arbeit war nur durch die Unterstützung vieler Menschen möglich, denen ich hiermit danken möchte. Zuallererst möchte ich Ferenc danken, dass er die Arbeit betreut hat und ich in der Gruppe arbeiten konnte. Ich habe durch das tolle Umfeld viel gelernt! Außerdem möchte ich meinem direkten Betreuer Ioachim herzlich danken. Im Rahmen der Doktorarbeit ist ein tolles Team rund um die Cavities entstanden, was wesentlich Dir zuzuschreiben ist. Danke für die Unterstützung, von der Laborarbeit bis zum Verbessern meiner Schreibkunst! Als ich angefangen habe, bestand das Team neben Ioachim nur aus Simon und Herrn Fill, der inzwischen ins Mid-IR Team gewechselt ist. Kurz darauf stieß Niko zu uns, zunächst als HiWi, dann als Masterand und inzwischen als Doktorand. Vielen Dank für die tolle Zeit! Inzwischen ist das Team um Tobi, Maxi, Christina und Stephan gewachsen. Auch euch danke ic...