Book excerpt: This dissertation discusses that, as market designers and experimental economists, we must be willing to accept that individuals may not play complicated equilibrium strategies. This departure from classical game theory predictions leaves us with a dilemma as market designers. One approach could be to make optimal play in matching algorithms as easy as possible by constructing strategyproof mechanisms, where individuals have dominant strategies of truthfully stating their preferences. We develop novel strategyproof algorithms in the first chapter of this dissertation that can be used in markets seeking to meet distributional goals. Many prominent markets in the field that would benefit from our mechanisms are currently inefficiently using strategyproof algorithms (presumably because they value such a strong incentive property); our contribution is to preserve strategyproofness but improve efficiency. In the second chapter of the dissertation, we show that efficiency can be improved even further if we are willing to sacrifice strategyproofness. Venturing into manipulable (non-strategyproof) algorithms can be risky, however. In manipulable mechanisms, individuals may state their preferences in ways that ultimately make themselves (and others) worse off in comparison to their outcomes in strategyproof algorithms. Whether or not we should even consider manipulable algorithms is a big question in market design. The second chapter in this dissertation finds that subjects actually fare better on average when we move away from strategyproofness. The welfare-improving algorithms we study discuss in the second chapter lead many individuals to manipulate their preferences in the same ways, suggesting that the mechanisms' specific designs stimulate non-random non-equilibrium behavior. As market designers, we can use these systematic deviations from equilibrium to develop algorithms that are best suited for the types of agents in the population. In particular, as market designers we should start thinking about creating algorithms for agents who play according to well-documented behavioral game theory models, such as the level-k model that explains many subjects' actions in the third chapter of this dissertation. Altogether, there is much additional theoretical and experimental work that needs to be done to fully understand (1) the way subjects behave in strategic settings and (2) which mechanisms will lead to the highest realized levels of agent welfare in practice. Fortunately, making progress on either of these questions will simultaneously advance our position on solving the other. It seems there is much potential for future work to make valuable contributions to what may ultimately become known as ``behavioral market design.''.