The interaction of the water dimer with both the olefinic and aromatic pi systems (ethene, benzene, toluene, fluorobenzene, and p-difluorobenzene) has been investigated using both the supermolecular [second-order Moller-Plesset (MP2)] and perturbational (symmetry adapted perturbation theory) approaches. The geometry optimizations, harmonic vibrational frequencies, and the components of the binding energy were evaluated using fairly large basis sets (6-31 + G* and aug-cc-pVDZ). The minimum energy structures obtained at the MP2/6-31 + G* and MP2/aug-cc-pVDZ levels of theory indicate that the water dimer exhibits a pi-type of interaction with ethene, benzene, and toluene and a sigma-type of interaction with both fluorobenzene and p-difluorobenzene. This is demonstrated from the vibrational frequencies which are in good agreement with the experimentally determined numbers. Our calculations indicate that the nature and strength of the interaction of the donor water molecule (water dimer) with the pi system has a significant bearing on the total binding energy of the complex. Apart from the interaction of the water dimer with the pi system, we also show how this interaction influences the hydrogen bond characteristics of the water dimer by evaluating the hydrogen bond strengths.