In C3 plants, photorespiration is an energy-expensive process, including the oxygenation of ribulose-1,5-bisphosphate (RuBP) by ribulose 1,5-bisphosphate carboxylase/oxygenase (Rubisco) and the ensuing multi-organellar photorespiratory pathway required to recycle the toxic byproducts and recapture a portion of the fixed carbon. Photorespiration significantly impacts crop productivity through reducing yields in C3 crops by as much as 50% under severe conditions. Thus, reducing the flux through, or improving the efficiency of photorespiration has the potential of large improvements in C3 crop productivity. Here, we review an array of approaches intended to engineer photorespiration in a range of plant systems with the goal of increasing crop productivity. Approaches include optimizing flux through the native photorespiratory pathway, installing non-native alternative photorespiratory pathways, and lowering or even eliminating Rubisco-catalyzed oxygenation of RuBP to reduce substrate entrance into the photorespiratory cycle. Some proposed designs have been successful at the proof of concept level. A plant systems-engineering approach, based on new opportunities available from synthetic biology to implement in silico designs, holds promise for further progress toward delivering more productive crops to farmer's fields.