Solid-state electromechanical smart material actuators are versatile as they permit diverse shapes and designs and can exhibit different actuation modes. An important advantage of these actuators compared to conventional ones is that they can be easily miniaturized to a sub-millimeter scale. In recent years, there has been a great surge in novel liquid pumps operated by these smart material actuators. These devices create opportunities for applications in fields ranging from aerospace and robotics to the biomedical and drug delivery industries. Although these have mainly been prototypes, a few products have already entered the market. To assist in the further development of this research track, we provide a taxonomy of the electromechanical smart material actuators available, and subsequently focus on the ones that have been utilized for operating pumps. The latter includes unidirectional shape memory alloy-, piezoelectric ceramic-, ferroelectric polymer-, dielectric elastomer-, ionic polymer metal composite- and conducting polymer-based actuators. Their properties are reviewed in the context of engineering pumps and summarized in comprehensive tables. Given the diverse requirements of pumps, these varied smart materials and their actuators offer exciting possibilities for designing and constructing devices for a wide array of applications.