pi-Electron delocalization exerts one of the most significant structure or energy influences in organic chemistry. Apart from determining the shapes of alkenes and alkynes, the planarity of aromatic molecules is a hallmark of pi-electron delocalization. Huckel's rules for aromaticity are easily applied in the teaching of undergraduates, but occasionally, some interesting discussions arise when questions are asked about some potentially aromatic nonbenzenoid molecules and antiaromaticity. Molecular modeling, using the X-ray crystallographic coordinate data for a representative sample of these interesting molecules, will lead to a greater understanding of just how these pi-systems achieve stability. (Contains 14 figures and 9 schemes.)