Nano- and micro-scale optical systems, with feature sizes comparable to the wavelength of light, represent a powerful way to control the properties of optical fields. For example, photonic crystals (periodically patterned dielectrics) possess optical properties linked to their underlying geometry that can significantly depart from those of the dielectric material from which they are patterned. In the field of quantum optics with ultracold atoms, where the goal is often to create a system where atoms and photons interact strongly compared to dissipation, nano-photonic systems based on photonic crystals are attractive because they can strongly confine optical fields with little loss, permit long-range photon-mediated interactions between atoms, and are more easily scalable to complex systems. In this colloquium, I will introduce this exciting field and describe work in the Caltech Quantum Optics Group for designing, fabricating, and utilizing photonic crystals for trapping atoms and realizing strong atom-photon interactions.