The ultrafast interaction of x rays with matter is a new field that is enabled experimentally by novel light sources like free-electron lasers and is essentially unexplored theoretically. Exciting new possibilities open up in many areas of science for which the theoretical basis for their understanding needs to be established. This is the goal of the presented proposal with respect to fundamental questions in atomic, molecular, and optical physics. Proceeding from the basics to more complex scenarios, I will study the fundamental nonlinearities in the interaction of x rays with matter that manifest in multiphoton and multielectron processes. First, I will study the absorption of x rays by molecules, including multiple core hole formation and decay, and few-x-ray-photon absorption. Second, I will combine x rays with a high-intensity optical laser, a two-color problem. Specifically, I will establish quantum optics for x rays by “watching” electromagnetically induced transparency for x rays in real time with ultrashort x-ray pulses. Then, I will examine the manipulation of the high harmonic generation process with x rays and explore its potential for providing light with unprecedented traits at such energies; notably, the generation of attosecond x-ray pulses may become feasible.