In recent years, a wide range of single-molecule devices has been realized, enabled by technological advances combined with the versatility offered by synthetic chemistry. In particular, single-molecule diodes have attracted significant attention with an ongoing effort to increase the rectification ratio between the forward and reverse current. Various mechanisms have been investigated to improve rectification, either based on molecule-intrinsic properties or by engineering the coupling of the molecule to the electrodes. In this perspective, we first provide an overview of the current experimental approaches reported in literature to achieve rectification at the single-molecule level. We then proceed with our recent efforts in this direction, exploiting the internal structure of multi-site molecules, yielding the highest rectification ratio based on a molecule-intrinsic mechanism. We introduce the theoretical framework for multi-site molecules and infer general design guidelines from this. Based on these guidelines, a series of two-site molecules have been developed and integrated into devices. Using two- and three-terminal mechanically controllable break junction measurements, we show that depending on the on-site energies, which are tunable by chemical design, the devices either exhibit pronounced negative differential conductance, or behave as highly-efficient rectifiers. Finally, we propose a design of a single-molecule diode with a theoretical rectification ratio exceeding a million.