This chapter begins by establishing the effect of constituents with opposite Poisson’s ratio signs on the effective moduli of composite properties. Results show that the effective Young’s modulus of continuous unidirectional fiber composites in the fiber direction and that for laminates of isotropic laminas in the in-plane direction exceeds the rule of mixture prediction, especially when the difference between Young’s moduli and Poisson’s ratios between the constituents are small and large, respectively. For laminates of isotropic laminas with opposing Poisson’s ratio signs, the effective Young’s modulus in the out-of-plane direction not only exceeds the inverse rule of mixture but also the direct rule of mixture, and this is especially so when the difference between the Young’s modulus of individual laminas is insignificant. The conditions that lead to further counter-intuitive properties whereby the in-plane laminate modulus exceeds the modulus of the stiffer phase is established, followed by an example in which the maximum point of the laminate modulus takes place when the volume fraction of the stiffer phase is lower than the volume fraction of the more compliant phase. Thereafter, investigation on laminates of isotropic laminas with alternating signs of Poisson’s ratio and alternating signs of coefficient of thermal expansion (CTE) gives results of extreme overall CTE. Finally, a review is done for investigation on conventional composites that lead to auxetic properties.