Plasmonic nanostructures have attracted considerable attention for their ability to couple with light and provide strong electromagnetic energy confinement at subwavelength dimensions. The absorbed portion of the captured electromagnetic energy can lead to significant heating of both the nanostructure and its surroundings, resulting in a rich set of nanoscale thermal processes that defines the subfield of thermoplasmonics with applications ranging from nanochemistry and nanobiology to optoelectronics. Recently, phononic nanostructures have started to attract attention as a platform for manipulation of phonons, enabling control over heat propagation and/or mechanical vibrations. The complex interaction phenomena between photons, electrons, and phonons require appropriate modelling strategies to design nanodevices that simultaneously explore and exploit the optical, thermal, and mechanical degrees of freedom. Examples of such devices are micro- and nanoscale opto-thermo-mechanical systems for sensing, imaging, energy conversion, and harvesting applications. Here, an overview of the fundamental theory and concepts crucial to the modelling of plasmo-phonon devices is provided. Particular attention is given to micro- and nanoscale modelling frameworks, highlighting their validity ranges and the experimental works that contributed to their validation and led to compelling applications. Finally, an open-ended outlook focused on emerging applications at the intersection between plasmonics and phononics is presented.