Major advances in modeling and control will be required to meet future technical challenges in microelectronics manufacturing. This paper reviews the recent applications of fundamental mathematical modeling to unit operations such as crystal growth, lithography, chemical vapor deposition and plasma etching, where there have been some notable successes. Important characteristics of these processes are identified, and the evolution of the standard multiwafer reactor to single wafer reactors processing larger wafers is discussed. The implementation of closed-loop control on key unit operations in microelectronics manufacturing has been extremely limited due to a lack of suitable on-line measurements. There remains considerable promise for application of modern control and optimization techniques in manufacture of integrated circuits.