Micro- and nanomechanical resonators are currently receiving enormous interest due to their potential as a new class of quantum systems, with possible impact ranging from the foundations of quantum physics, quantum limited sensing and quantum information processing. A particularly successful system is the optomechanical oscillator, where the radiation pressure of light is used to manipulate and read-out the dynamics of the mechanical system. To date experiments have demonstrated individually each key ingredient for the preparation of optomechanical systems in the quantum regime, however still operating in the classical domain. In this proposal we want to take the field one step further, by increasing the optomechanical coupling strength to a level where single-photon effects become dominant. In this regime, one can exploit the full non-linear character of the interaction. This will be achieved by designing and optimizing optomechanical crystals, a novel system where the photonic and phononic modes are localized in a single device, which have recently been developed by the outgoing host. These systems currently outperform all existing optomechanical devices in coupling strength and are ideal candidates for single-photon quantum optomechanics. Envisioned experiments range from answering fundamental questions in quantum physics to quantum information processing tasks - optomechanical crystals can be engineered on-chip, with the potential for realizing a mass-maufacturable quantum technology. Also, the frequencies of the optomechanical crystals can be designed to allow for ground-state preparation when cooled in a dilution refrigerator, which is an enabling regime for observing quantum effects even with coherent optical input fields. The ideal match of the expertise of the outgoing host and the experienced researcher in quantum optics and (quantum) opto-mechanics will result in ground-breaking new developments in this young and rapidly expanding field.