Poisson's ratio had long been considered to be an intrinsic material property, confined within a narrow domain and governed solely by the geometry of interatomic bonds. Materials with designed heterogeneity allow for control over the Poisson's ratio. Poisson's ratios of any value within the thermodynamically admissible domain may be attained, including negative Poisson's ratio (termed auxetic). In this article, we discuss the role of Poisson's ratio in elasticity, two-dimensional and three-dimensional materials, phase transformations, underlying causes in the microstructure, and other negative physical properties.