In the growing fields of wearable robotics, rehabilitation robotics, prosthetics, and walking k robots, variable stiffness actuators (VSAs) or adjustable compliant actuators are being designed and implemented because of their ability to minimize large forces due to shocks, to safely interact with the user, and their ability to store and release energy in passive elastic elements. This review article describes the state of the art in the design of actuators with adaptable passive compliance. This new type of actuator is not preferred for classical position-controlled applications such as pick and place operations but is preferred in novel robots where safe human- robot interaction is required or in applications where energy efficiency must be increased by adapting the actuator's resonance frequency. The working principles of the different existing designs are explained and compared. The designs are divided into four groups: equilibrium-controlled stiffness, antagonistic-controlled stiffness, structure-controlled stiffness (SCS), and mechanically controlled stiffness.