The ability to bend, stretch, and roll metamaterial devices on flexible substrates adds a new dimension to aspects of manipulating electromagnetic waves and promises a new wave of device designs and functionalities. This work reviews terahertz and optical metamaterials realized on flexible and elastomeric substrates, along with techniques and approaches to lend tunability to the devices. Substrate electromagnetic and mechanical characteristics suitable for flexible metamaterials are summarized for readers, followed by fabrication and processing techniques, and finally novel approaches used to-date to attain tunability. Future directions and emerging areas of interests are identified with these promising to transform metamaterial design and translate metamaterials into practical devices.