© 2020 Elsevier Ltd Thermoelectric geometry and structure optimization are vital research areas which are being explored extensively in recent years due to significant performance enhancement achieved. However, the lack of a single review paper on this key area is a huge gap identified. Therefore, this review presents a first of its kind in-depth analysis of the start of art in thermoelectric geometry and structure optimization. The four main parameters including leg length or height, cross-sectional area, number of legs and leg shape which are paid attention to during optimization of thermoelectric geometry are discussed in detail. In addition, a review of the different thermoelectric structure available in literature such as flat plate, annular, segmented, cascaded, corrugated, concentric, linear, flexible and micro thermoelectric generators and coolers is presented. Furthermore, special attention is paid to both electrical and mechanical performance enhancement obtainable from thermoelectric geometry and structure optimization. A review of thermal stress optimization is presented alongside other optimization including contact resistance, heat pipe, pulsed heating and cooling. Geometry and structure optimization methods including three-dimensional finite optimization and multi-objective optimization are discussed in detailed and the most significant results obtained from the literature review are presented. This comprehensive review will be a valuable and essential reference literature on all issues relating to thermoelectric geometry and structure optimization.