Pump-controlled hydraulic cylinder drives may offer improved energy efficiency, compactness, and plug-and-play installation compared to conventional valve-controlled hydraulic systems and thus have the potential of replacing conventional hydraulic systems as well as electro-mechanical alternatives. Since the late 1980s, research into how to configure the hydraulic circuit of pump-controlled cylinder drives has been ongoing, especially in terms of compensating the uneven flow requirements required by a differential cylinder. Recently, research has also focused on other aspects such as replacing a vented oil tank with a small-volume pressurized accumulator including the consequences of this in terms of thermal behavior. Numerous references describe the advantages and shortcomings of pump-controlled cylinder drives compared to conventional hydraulic systems or electro-mechanical drives. This paper presents a throughout literature review starting from the earliest concepts based on variable-displacement hydraulic pumps and vented reservoirs to newer concepts based on variable-speed electric drives and sealed reservoirs. By classifying these drives into several proposed classes it is found that the architectures considered in the literature reduce to a few basic layouts. Finally, the paper compares the advantages and shortcomings of each drive class and seek to predict future research tasks related to pump-controlled cylinder drives.