We consider an assemble-to-order (ATO) system with multiple products and components having guaranteed maximum delivery leadtimes. For such a system, the first-order operational challenge is to balance the demand and supply of components through pricing and supply contracts (or capacity planning). However, due to stochastic fluctuations in supply and demand, component shortages occur. Then, the manufacturer must dynamically allocate scarce components to customer orders for various products, and/ or pay to expedite component production. In practice, many firms adopt simple static rules to sequence customer orders for assembly, such as FIFO, and expedite components on an ad hoc basis. Recently, Dell has begun to prioritize customer orders dynamically, based on component availability. However, dynamic control of an ATO system is difficult, and theory is needed to guide business practice. We undertake a holistic analysis of a high-volume ATO system. Our objective is to maximize expected infinite horizon discounted profit subject to assembling orders within a guaranteed maximum delivery leadtime. Our key assumption is that the inter-arrival time between customers is small compared to guaranteed delivery leadtimes, meaning the ATO system is high-volume. (This is certainly true for Dell; its new OptiPlex assembly plant assembles more than 20,000 computers per day whereas a customer's order is guaranteed to ship within 10 days.) We first establish that any revenue-maximizing strategy requires optimal prices and component production rates to be close. In such a regime, diffusion approximations are extremely accurate. Furthermore, in this regime, the system exhibits a reduction in problem dimensionality. This simplifies the dynamic control problem and allows us to provide easily implementable policies for sequencing customer orders and expediting components that are asymptotically optimal in the heavy traffic limit. We finish by characterizing the structure of near-optimal inventory policies. By taking account of important component dependencies, the near-optimal inventory policy will outperform any base stock policy.