Ideas from quantum optics based on coherence and interference play an important role in studying, controlling, and utilizing quantum dynamics. Recent improvements in existing and upcoming x-ray light sources prompt the question, whether such techniques could also be applied in the hard x-ray regime [1]. This would not only be essential for fully exploiting the potential of these machines, but could also pave the way for new applications. In turn, x-ray quantum optics could also evolve into a promising platform for the study of light-matter interactions.  One particular branch is the interaction of x-rays with large ensembles of Mössbauer nuclei. These nuclei feature resonances with exceptionally narrow linewidth, and form the basis for a broad range of applications in the natural sciences, particularly also in material science and condensed matter physics.  In this talk, I will introduce the basic concepts and ideas of nuclear quantum optics, and outline recent theoretical and experimental progress as well as challenges. In particular, I will focus on the problem that the spectra of short x-ray pulses delivered by state-of-the-art sources are orders of magnitude broader in energy than the narrow resonances. Thus, only a tiny fraction of the photons interact resonantly with the sample, while the vast majority of photons form an off-resonant background. I will show how the precisely controlled mechanical motion of a resonant target can be used to shape the spectrum of a given x-ray pulse, such that the number of resonant photons in the pulse is significantly increased [2]. This increased intensity results in shorter measurement times, and enables measurements with presently too low signal rates.  Next, I will show how mechanical motions of a suitable target allow for the generation of tunable phase-coherent x-ray double-pulse sequences, and demonstrate that these double-pulses can be used to coherently control excitons in large ensembles of atomic nuclei. In a proof-of-principle experiment, we find clear signatures of basic light-matter interactions such as stimulated emission and absorption between the nuclei and the x-rays [3].