Ultracold quantum gases with long-range interactions can spontaneously form crystalline structures when the strength of quantum fluctuations is sufficiently low. I will discuss the properties of this phase transition in the case of strongly interacting Rydberg atoms, where Rydberg excitations are created by laser driving . For 1D lattice models, there is a series of additional phase transitions between commensurate and incommensurate crystals . Finally, I will present a proposal for the creation of large crystalline structures of polar molecules, using nonadiabatic driving of rotational transitions . H. Weimer, R. Löw, T. Pfau, H. P. Büchler, Phys. Rev. Lett. 101, 250601 (2008). H. Weimer, H. P. Büchler, Phys. Rev. Lett. 105, 230403 (2010). M. Lemeshko, R. V. Krems, H. Weimer, Phys. Rev. Lett. (to be published), arXiv:1203.0010.