In the economic theory of mechanism design, the goal is to elicit private information from each of multiple agents in order to select a desirable system wide outcome, and despite agent self-interest in promoting individually beneficial outcomes. Auctions provide a canonical example, with information elicited in the form of bids, and an allocation of resources and payments defining an outcome. Indeed, one aspect of the emerging interplay between machine learning (ML) and mechanism design (MD) arises by interpreting auctions as a method for learning agent valuation functions. In addition to seeking sufficient accuracy to support optimal resource allocation, we require for incentive compatibility that prices are insensitive to the inputs of any individual agent and find an interesting connection with regularization in statistical ML. More broadly, ML can be used for de novo design, in learning payment rules with suitable incentive properties. Ideas from MD are also flowing into ML. One example considers the use of mechanisms to elicit private state, reward and transition models, in enabling coordinated exploration and exploitation in multi-agent systems despite self-interest. Another application is to supervised learning, where labeled training data is elicited from self-interested agents, each with its own objective criterion on the hypothesis learned by the mechanism. Looking ahead, a tantalizing challenge problem is to adopt incentive mechanisms for the design of robust agent architectures, for example in assigning internal rewards that promote modular intelligent systems.