One of the ultimate goals of molecular electronics is to create technologies that will complement-and eventually supersede-Si-based microelectronics technologies. To reach this goal, electronic properties that mimic at least some of the electrical behaviors of today's semiconductor components must be recognized and characterized. An outstanding example for one such behavior is negative differential conductance (NDC), in which an increase in the voltage across the device terminals results in a decrease in the electric current passing through the device. This overview focuses on the NDC phenomena observed in metal-single molecule-metal molecular junctions, and is roughly divided into two parts. In the first part, the central experiments which demonstrate NDC in single-molecule junctions are critically reviewed, with emphasis on the main observations and their possible physical origins. The second part is devoted to the theory of NDC in single-molecule junctions, where simple models are employed to shed light on the different possible mechanisms leading to NDC.