With rapid progress in quantum technology, focus is shifting from demonstrations on a small number of noisy qubits towards interesting application problems, of academic or commercial interest, where a quantum computer can outperform even the best classical supercomputer. Comparing current classical computers with optimistic assumptions for future quantum computers I will present criteria for achieving such practical quantum advantage and will argue that “small data” problems with superquadratic quantum speedups are the most promising candidates. The simulation of quantum systems, with applications to condensed matter physics, materials science of chemistry is one such application area. I will present recent progress on quantum algorithms for chemistry and discuss that realizing such a quantum advantage will require more than just a quantum algorithm and quantum computer.