This article presents a methodology for reengineering complex computer systems. An important aspect of the reengineering methodology is the mission-critical software architecture (MCSA), a hierarchical view of complex systems that includes the levels of task clusters, tasks, packages, procedures, and statements. Reverse engineering identifies system attributes at each level of the MCSA. After reverse engineering, the system's software design is restructured to increase layering and concurrency, and code is generated to effectively use language constructs. Given the code of tasks and packages, program components are partitioned into tightly coupled clusters, and clusters are assigned to hardware processors. A key element of the reengineering methodology is a set of concurrency metrics for guiding the transformation tasks. The metrics are defined at each level of the MCSA and enable the assessment of concurrency within a component or a cluster, and also among components and clusters.