The science of x-rays is by now over 125 years old, starting with Wilhelm R€ ontgen's discovery of x-rays in 1895, for which R€ ontgen was awarded the first Nobel Prize in Physics. X-rays have fundamentally changed the world in areas, including medical imaging, security scanners, industrial inspection, materials development, and drugs spectroscopy. X-ray science has been so far responsible for over 25 Nobel Prizes in Physics, Chemistry, and Medicine/Physiology. With x-ray generation being a highly commercialized, widely adopted technology, it may appear that there is little left to discover regarding the fundamentals of x-ray science. Contrary to this notion, recent years have shown renewed interest in the research and development of innovative x-ray concepts. We highlight, in this Perspective, promising directions for future research in x-ray science that result from advances in quantum science and in nanomaterials. Specifically, we describe three key opportunities for advancing x-ray science in the near future: (1) emerging material platforms for x-ray generation, especially 2D materials and their heterostructures; (2) free-electron-driven emission of entangled photon-photon and electron-photon pairs for x-ray quantum optics; and (3) shaping free-electron wavepackets for controllable x-ray emission. These research directions could lead to improvements in x-ray resonance fluoroscopy, high-contrast x-ray imaging, stimulated coherent x rays, x-ray superradiance, and other prospects for x-ray quantum optics.