Subject and Outline -- Kanban-Controlled Manufacturing Systems: Basic Version and Variations -- Literature Review: Models of Kanban Systems -- New Models of Kanban Systems: A Construction-Kit Approach -- Components: Basic Building Blocks -- Subassemblies: Models of Multi-Product Manufacturing Facilities -- Composite Models: Models of Multi-Stage Kanban Systems -- Extended Application: Models of Systems with Multi-Product Manufacturing Facilities in Series -- Accuracy of the Models: Numerical Results -- Application of the Models: Analysis of System Behavior -- Summary and Directions for Future Research.5th Werner Kern Award for Productivity Research 2005 Kanban control systems bear a great potential to significantly improve operations. A company may reap the full benefits of kanban control only after determining an optimal or near-optimal system configuration. To do that, methods are needed to evaluate the performance and operating costs of individual system configurations. We propose an innovative construction-kit approach that enables us to build stochastic analytical models of a large class of single- and multi-product kanban systems. The presented construction-kit approach may be extended and augmented in various directions. .