Anticancer agents used in combination are fundamental to successful cancer treatment, particularly in a curative setting. For dual-agent phase I trials, the goal is to identify drug doses and schedules for further clinical testing. However, current methods for establishing the recommended phase II dose for agents in combination can fail to fully explore drug interactions. With increasing numbers of anticancer drugs requiring testing, new adaptive model-based trial designs that improve on current practice have been proposed, although uptake has been minimal. We describe the methods available and discuss some of the opportunities and challenges faced in dual-agent phase I trials, as well as giving examples of trials in which adaptive designs have been implemented successfully. Improving the design and execution of phase I trials of drug combinations critically relies on collaboration between the statistical and clinical communities to facilitate the implementation of adaptive, model-based designs.