In the medical field and in soft robotics, flexible devices are required for safe human interaction, while rigid structures are required to withstand the force application and accuracy in motion. This paper aims at presenting controllable stiffness mechanisms described in the literature for applications with or without shape-locking performances. A classification of the solutions based on their working principle is proposed. The intrinsic properties of these adaptive structures can be modified to change their mechanical characteristics from a geometrical point of view or equivalent elastic properties (with internal mechanisms or with a change in material properties). These solutions are compared quantitatively, based on selected criteria linked to the medical field as the stiffness range, the activation time and the working conditions. Depending on the application and its requirements, the most suitable solution can be selected following the quantitative comparisons. Several applications of these tunable stiffness structures are proposed and illustrated by examples of the literature.