This paper presents a detailed, yet by no means exhaustive, survey of the application of mathematical modeling and simulation to dynamic problems in various engineering fields. After a brief discussion of the steps involved in the modeling process, applications are cited in the fields of aircraft design, control systems, circuit analysis and synthesis, structures, process control, vehicles other than aircraft, and human performance. Detailed consideration is given to two examples: design and optimization of an aircraft control system, and prediction of nonperiodic structural loading on a rotary wing. Finally, it is suggested how techniques successfully applied in other fields can aid in automotive vehicle safety studies.