  Refraction at the interface between two materials is fundamental to the
interaction of light with photonic devices and to the propagation of light
through the atmosphere at large. Underpinning the traditional rules for the
refraction of an optical field is the tacit presumption of the separability of
its spatial and temporal degrees-of-freedom. We show here that endowing a
pulsed beam with precise spatio-temporal spectral correlations unveils
remarkable refractory phenomena, such as group-velocity invariance with respect
to the refractive index, group-delay cancellation, anomalous group-velocity
increase in higher-index materials, and tunable group velocity by varying the
angle of incidence. A law of refraction for `space-time' wave packets
encompassing these effects is verified experimentally in a variety of optical
materials. Space-time refraction defies our expectations derived from Fermat's
principle and offers new opportunities for molding the flow of light and other
wave phenomena.
