Unlike many academic economists, Roth's graduate school work was not in economics specifically but instead in operations research, which is the study of optimizing processes such as networks and queues. (Roth received an undergraduate degree in operations research from Columbia University in 1971 and masters and doctoral degrees in the same field from Stanford University in 1973 and 1974, respectively.) He then went on to join the faculty of the University of Illinois and the University of Pittsburgh before transferring to Harvard Business School in 1998.
Roth's work in economics is unique not only because it combines elements of traditional economics with what he learned studying operations research, but also because much of his work is more focused on real-world solutions than it is on academic theory. Roth's main area of research is in designing algorithms for what are known as two-sided matching markets- i.e. markets where both the buyer and seller care specifically about the attributes of who they are paired up with. (These markets are obviously more complicated than ones where buyers and sellers will transact with anyone as long as it's at the right price.) More specifically, Roth works with markets such as those for kidney exchange or school choice where using prices as an allocation mechanism isn't an option for legal or logistical reasons.
The market for kidney exchange, for example, suffers from two serious limitations. The first is that, because people cannot be legally be compensated for their organs, there are far fewer kidney donors than there are patients in need of transplants. (Theoretically, monetary compensation would encourage more people to act as suppliers in this market.) The second problem is that, even when a donor is willing and able, he might not be a match for his intended recipient, and he likely won't be willing to donate to just anyone. Roth helps solve this problem by arranging pairs and chains of donors and recipients. The general logic is that, while a donor likely won't donate to a random stranger independently, he would probably do so if he knew that his donation enabled a donation on the part of another individual to the person he was initially trying to help. (The transplants are then performed simultaneously to ensure that no one reneges!) Many more transplant patients have been able to be matched with donors as a result of this system.
The markets for school choice and medical resident matching suffer from different but related issues. In these markets, parents and residents are presented with systems that gives them incentives to not represent their preferences truthfully (i.e. to game the system). This results in inefficient in the matching process. Roth, in contrast, developed algorithms for the schools and hospitals to use that are "strategy-proof"- in other words, that are most likely to give users what they want if they represent their preferences truthfully. These algorithms have resulted in better matches and increased welfare on the part of everyone involved.
Overall, Professor Roth is notable because his contributions are particularly significant both inside and outside of the academic world.