Quantitatively, a many-particle system is said to be hyperuniform if the variance of the number of points within a spherical observation window grows more slowly than the volume of the observation window. This definition is equivalent to a vanishing of the structure factor in the long-wavelength limit, and it has been extended to include heterogeneous materials as well as scalar, vector, and tensor fields. Disordered hyperuniform systems, were shown to be poised at an "inverted" critical point. They can be obtained via equilibrium or nonequilibrium routes, and are found in both classical physical and quantum-mechanical systems. Hence, the concept of hyperuniformity now connects a broad range of topics in physics, mathematics, biology, and materials science.