Several hundred organizations are now using prediction markets to forecast sales, project completion dates, and more. This number has been doubling annually for several years. Most, however, are simple prediction markets, with one market per number forecast, and several traders per market. In contrast, a single combinatorial prediction market lets a few traders manage an entire combinatorial space of forecasts. For millions of numbers or less, implementation is easy, and lab experiments have confirmed feasibility and accuracy. For larger spaces, however, many open computational problems remain.