A series of recent experimental and computational studies has explored how the dynamics of hydrogen abstraction from organic molecules are affected by the presence of functional groups in the molecule and by basic structural motifs such as strained ring systems. Comparisons drawn between reactions of Cl atoms with alkanes such as ethane, Cl + CH3CH3--> HCl + CH3CH2, which serve as benchmark systems, and with functionalized molecules such as alcohols, amines, and alkyl halides, Cl + CH3X --> HCl + CH2X (X = OH, NH2, halogen, etc.) expose a wealth of mechanistic detail. Although the scattering dynamics, as revealed from measured angular distributions of the velocities of the HCl with quantum-state resolution, show many similarities, much-enhanced rotational excitation of the HCl products is observed from reactions of the functionalized molecules. The degree of rotational excitation of the HCl correlates with the dipole moment of the CH2X radical and is thus attributed, at least in part, to post-transition-state dipole-dipole interactions between the separating, polar reaction products. This interpretation is supported by direct dynamics trajectories computed on-the-fly, and the HCl rotation is thus argued to serve as an in situ probe of the angular anisotropy of the reaction potential energy surface in the post-transition-state region. Comparisons between the dynamics of reactions of dimethyl ether and the three- and four-membered-ring compounds oxirane (c-C2H4O) and oxetane (c-C3H6O) raise questions about the role of reorientation of the reaction products on a time scale commensurate with their separation. The shapes and structures of polyatomic molecules are thus demonstrated to have important consequences for the stereodynamics of these direct abstraction reactions.