Since 1995, Magnetic Resonance Elastography (MRE) has been constantly developed as a non-invasive diagnostic tool for quantitative mapping of mechanical properties of biological tissues. Indeed, mechanical properties of tissues vary over five orders of magnitude (the shear stiffness is ranging from 10² Pa for fat to 10⁷ Pa for bones). Additionally, these properties depend on the physiological state which explains the granted benefit of MRE for staging liver fibrosis and its potential in numerous medical and biological domains. In comparison to the other modalities used to perform such measurement, Magnetic Resonance (MR) techniques offer the advantages of acquiring 3D high spatial resolution images at high penetration depth. However, performing MRE tissue characterization requires low frequency shear waves propagating in the tissue. Inducing them is the role of a mechanical actuator specifically designed to operate under Magnetic Resonance Imaging (MRI) specific restrictions in terms of electromagnetic compatibility. Facing these restrictions, many different solutions have been proposed while keeping a common structure: a vibration generator, a coupling device transmitting the vibration and a piston responsible for the mechanical coupling of the actuator with the tissue. The following review details the MRI constraints and how they are shaping the existing actuators. An emphasis is put on piezoelectric solutions as they solve the main issues encountered with other actuator technologies. Finally, flexible electroactive materials are reviewed as they could open great perspectives to build new type of mechanical actuators with better adaptability, greater ease-of-use and more compactness of dedicated actuators for MRE of small soft samples and superficial organs such as skin, muscles or breast.