Quantum technologies have seen a rapid developmental surge over the last couple of years. Though often overshadowed by quantum computation, quantum sensors show tremendous potential for widespread applications in chemistry and biology. One system stands out in particular: the nitrogen-vacancy (NV) center in diamond, an atomic-sized sensor allowing the detection of nuclear magnetic resonance (NMR) signals at unprecedented length scales down to a single proton. In this article, we review the fundamentals of NV center-based quantum sensing and its distinct impact on nano- to microscale NMR spectroscopy. Furthermore, we highlight and discuss possible future applications of this novel technology ranging from energy research, material science, or single-cell biology, but also associated challenges of these rapidly developing NMR sensors.