The imaging technique that uses electrical properties of materials such as electrical resistance measured on the surface/boundary to image subsurface details is called Electrical Resistance Tomography (ERT).  Over the last decade or more, ERT techniques have been investigated for applications in subsurface imaging of soils in geotechnical engineering, biomedical imaging of pulmonary edema of lungs and flows in arteries/veins, and for damage quantification for structural health monitoring.  Our interest is to develop ERT as a technique as a non-intrusive imaging and damage sensing technique for accurate quantification of damage initiation and growth in lab experiments for composite progressive failure.  The talk presents two optimization challenges addressed in our work to apply ERT to carbon fiber reinforced polymer composites-, namely optimization for inverse identification and optimization for sensor selection. The identification of damage in composites using surface measured electrical properties requires the solution of an inverse problem that is computationally expensive. Our work investigated use of different surrogate modeling techniques to address the computational challenges in the inverse optimization. In addition, hardware limitations often limit the number of electrode pairs that can be used for the sensing. Our research has developed a novel approach developed for optimal sensor selection for ERT.