The recent discoveries of mechanically flexible molecular crystals have fuelled a resurgence of research interest in molecular piezoelectrics. This has raised the quest to explore structure-property relations in molecular piezoelectric crystals, which remain largely obscure. Here, the fundamental structural features associated with organic molecular piezoelectric crystals are explored in relation to their mechanical and supramolecular flexibility. Along with the electrostatic properties such as molecular dipole moments and spontaneous crystal polarization, possible correlations of piezoelectric coefficients with intermolecular interaction topologies and their anisotropy point toward their link with mechanical flexibility in molecular crystals. In addition, the possible roles of crystal packing efficiency, lattice cohesive energies, Young's moduli, and its anisotropy from elastic tensors have been examined. This quantitative overview suggests that piezoelectric response in molecular materials is a complex interplay of several structural and electrostatic factors. Based on these analyses and the fundamental aspects of electromechanical coupling, it becomes apparent that combining mechanical flexibility and supramolecular chirality/polarity can be a promising approach to discovering soft molecular piezoelectrics for novel actuators and energy-harvesting materials.