This thesis is devoted to the development of ultrafast thin-disk lasers (TDL) oscillators and their use for intra-oscillator high-harmonic generation (HHG). The main motivation was to develop a simple and compact source of coherent extreme ultraviolet (XUV) light. Conventionally, coherent XUV radiation can be found in large scale synchrotron or free-electron laser facilities. Laser driven HHG systems have long strived to become a lab-scale alternative to these sources. The major challenge has been the low conversion efficiency of the HHG process and the high demands on the driving laser. With the advancing laser technology, this situation is rapidly improving and several state-of-the-art HHG systems can nowadays reach an XUV flux which is in certain aspects comparable to synchrotrons. The intra-laser-oscillator HHG approach is inspired by femtosecond enhancement cavities. Driving HHG inside an enhancement cavity allows for recycling the unconverted pulse energy, while increasing the available power by the cavity enhancement factor. An enhancement cavity, however, requires coherent coupling of the femtosecond pulses into the cavity which is a demanding task. The intra-oscillator HHG approach offers a simplified concept using directly the cavity of the laser instead of an external enhancement cavity. To achieve sufficiently high driving power for efficient intra-oscillator HHG, the existing TDL technology had to be significantly improved and optimized for intracavity performance. Within the scope of this thesis, a strong focus was placed on the development of the driving laser and significant progress has been achieved. To this purpose, we investigated and demonstrated Kerr lens modelocked TDL oscillators based on the gain material Yb:YAG, which achieved several records in terms of their output performance. Using our system we have demonstrated the shortest pulse duration of any TDL oscillator of 27 fs, as well as the highest average power in the sub-100-fs regime of 100 W and the highest peak power of 100 MW. The corresponding increase of intracavity performance of our laser allowed us to significantly improve the HHG operation in terms of the generated XUV flux and photon energies. Starting from 0.5 nW generated at 13 eV demonstrated five years ago, we have improved the XUV flux to 10 μW at 30 eV at the current state. Although this is not yet the highest performance among other HHG systems, the flux value is becoming competitive to the results of enhancement cavities operating at similar photon energy. The improved output performance of the demonstrated TDLs is also highly attractive for nonlinear conversion toward longer wavelengths of the electromagnetic spectrum. A part of this thesis is, thus, dedicated to terahertz generation. We have demonstrated the first TDL driven terahertz generation in 2018, through optical rectification in GaP. Later, we used the tunability and the high average power of our self-built TDL oscillator to experimentally investigate in detail the properties of optical rectification in GaP driven by 1- μm high-power Yb-based lasers. Finally, having the experience from intra-oscillator HHG, we have shown that the high-power driving laser can be replaced by driving the THz generation directly inside the cavity of a small KLM bulk laser oscillator.