Reputation systems are core components of online platform markets, incentivizing trust and trustworthiness. Small market design details may have large implications on the extent of trade and platform revenues. We selectively review our own and others’ research on the design of reputation mechanisms for platforms highlighting particular issues in the design of feedback systems which may affect feedback behavior and thus the informativeness and effectiveness of feedback information. We also discuss new research on conflict resolution mechanisms for platforms and the arguments for allowing reputation mobility. Finally, we conclude with implications for platform management and users.