The dispersion, which expresses the variation with wavelength of the guided-mode group velocity, is one of the most important properties of optical fibers. Photonic crystal fibers (PCFs) offer much larger flexibility than conventional fibers with respect to tailoring of the dispersion curve. This is partly due to the large refractive-index contrast available in silica/air microstructures, and partly due to the possibility of making complex refractive-index structures over the fiber cross section. We discuss the fundamental physical mechanisms determining the dispersion properties of PCFs guiding by either total internal reflection or photonic bandgap effects, and use these insights to outline design principles and generic behaviours of various types of PCFs. A number of examples from recent modeling and experimental work serve to illustrate our general conclusions.