An essential feature of hyperuniform systems is their scaling of the number variance σ σ N 2 ( R ) for large radii or, equivalently, of the structure factor S ( k ) for small wave numbers. If we consider hyperuniform systems that are characterized by a power-law behavior of the structure factor close to the origin: S ( k ) ∼ ∼ | k | α α for k → → 0 with a constant 0 < α α < ∞ ∞ , then there are three distinct scaling behaviors that define three classes of hyperuniformity : σ σ N 2 ( R ) ∼ ∼ { R d − − 1 , α α > 1 ( CLASS I ) R d − − 1 ln ⁡ ⁡ R , α α = 1 ( CLASS II ) R d − − α α , 0 < α α < 1 ( CLASS III ) Examples are known for all three classes of hyperuniformity.