Complex functional oxides provide key functionality for electrochemical energy conversion and storage devices, chiefly as the electrodes or electrolytes of solid oxide fuel cells and lithium ion batteries. For both of these applications of energy conversion and storage, the functional response depends directly on ion transport through the materials. For portable energy conversion and storage devices, there is an additional motivation for thin film forms of such materials (for smaller and lighter devices), and for electrochemical cycling (energy conversion startup-shutdown or energy storage charge-discharge cycles). It is now appreciated that there can exist strong coupling between the electrochemistry and cycling history of such oxides and the mechanical properties and deformation of such oxides under operando conditions. Here we discuss recent progress in experimental and analytical approaches to quantify such coupling between mechanics and electrochemical cycling history in select oxides used as materials in solid oxide fuel cells -- which breathe oxygen and exhibit point defect-dependent mechanical and electronic properties -- and in batteries -- which includes the solid electrolytes considered in solid-state batteries. Through the range of in situ characterization approaches that can correlate mechanics and electrochemistry at the nanoscale, we discuss how this provides new opportunities for design of both key materials and new structures for electrochemically driven devices.