Actuation is an essential function of any artificial or living machine, allowing its movement and its interaction with the surrounding environment. Living muscles have evolved over millions of years within animals as nature's premier living generators of force, work and power, showing unique characteristics in comparison with standard artificial actuators. Current actuation technologies actually represent a real bottleneck in many robotics and ICT applications, including the bio-inspired ones. Main limitations involve inertia and backdrivability, stiffness control and power consumption. The development of novel actuators able to better mimic or even to overcome living muscle performances would open new horizons in robotics and ICT technologies: these components would allow the raise of a new generation of machines, with life-like movements and outstanding performances. An innovative solution to achieve this goal is represented by the merging between artificial and living entities, towards the realization of bio-hybrid devices. The aim of the present article is to describe the scientific and technological efforts made by researchers in the last two decades to achieve cell- or tissue-based actuators, with the dream of matching or outperforming natural muscles and to efficiently power micro- and mini-devices. The main challenges connected to the development of a cell-based actuator are highlighted and the most recent solutions to this scientific/technological problem are depicted, reporting advantages and drawbacks of each single approach. Future perspectives are also described, envisioning bio-hybrid actuators as key components of a new generation of machines able to show life-like movements and behaviors.