At Brigham Young University researchers are using origami techniques to develop new medical tools that are much smaller than existing devices. They’re currently working with Intuitive Surgical, makers of the popular da Vinci robotic surgical systems, to license out some of their designs. As an example, the BYU engineers made grippers for the da Vinci that are pretty small (3mm in diameter) compared even to the already tiny grippers found within the robotic system. 
They avoid traditional components found in mechanical devices and instead rely on the natural material flexion that origami is famous for.
The team is also working on a new approach for spinal disc replacement that would rely on inserting a flat device that would expand and fill in the space of a natural disc. It consists of two parts that when expanded look like two half domes pressing and rocking against each other.
Here’s video of some of the projects the BYU researchers are working on:
More at BYU…