The next decade will see an abundance of new intelligent systems, many of which will be market-based. Soon, users will interact with many new markets, perhaps without even knowing it: when driving their car, when listening to a song, when backing up their files, or when surfing the web. We argue that these new systems can only be successful if a new approach is chosen towards designing them. In this paper we introduce the general problem of "Hidden Market Design." The design of a "weakly hidden" market involves reducing some of the market complexities and providing a user interface (UI) that makes the interaction seamless for the user. A "strongly hidden market" is one where some semantic aspect of a market is hidden altogether (e.g., budgets, prices, combinatorial constraints). We show that the intersection of UI design and market design is of particular importance for this research agenda. To illustrate hidden market design, we give a series of potential applications. We hope that the problem of hidden market design will inspire other researchers and lead to new research in this direction, paving the way for more successful market-based systems in the future.