The chapter discusses the problems of modeling, control, and decision support in complex dynamic systems from a general system theoretic point of view, with special emphasis on methodological aspects. We consider the main characteristics of complex systems and of system approach to complex system study. Then the chapter continues with the general dynamic modeling and simulation technique for complex hierarchical systems functioning in control loop. The proposed technique is based on the information-mathematical models and described in terms of the hierarchical state transition diagrams. The methodology is sufficiently abstract to allow both qualitative and quantitative analysis of system state dynamics and control through hierarchical scenario calculus. The evaluation of different scenarios is defined by the multiple criteria vector-functions related to the efficiency of control strategies and time required for system goals achievement. We also offer general architectural and structural models of computer information system intended for simulation and decision support in complex systems.