We report Density Functional Theory (DFT) studies of the dipole polarizabilities of benzene, furan and thiophene together with a number of substituted and related systems. All geometries were optimized (and characterized) at the B3LYP/6-311g(2d,1p) level of theory and polarizabilities then calculated with B3LYP/6-311++G(2d,1p). For the R-ring systems we find group polarizabilities in the order R = NO 2 ∼ OCH 3 ∼ CN ∼ CHO > NH 2 > OH > H = 0. For systems R-ring-R, <α> differs little from the additivity model, with small positive and negative increments. For systems D-ring-A (where D and A are deactivating and activating groups) we find a positive enhancement to <α> over and above the value expected on the basis of pure additivity for all pairs A and D studied. This enhancement can be increased greatly by extending the length of the conjugated chain to D-ring-CH=CH-ring-A and D-ring-N=N-ring-A systems. Empirical models of polarizability such as AM1 agree badly with the DFT calculations in an absolute sense but give excellent statistical correlation coefficients. Calculated <α>'s also agree well in a statistical sense with the molecular volumes calculated from molecular mechanics force fields Analysis of the results in terms of the π electrons alone is not satisfactory.