O the past 25 years a great body of knowledge has been built up on the subject of feedback control of linear, time-invariant dynamic systems. This knowledge plays an important role in our technology, and engineering schools recognize this fact by teaching courses in this area. However, many dynamic systems, particularly aerospace systems, are nonlinear and/or time-varying, and the techniques for analysis and design of linear, time-invariant control systems are, in general, not applicable to these more complicated systems. The appearance of practical, high-speed digital computers in the 1950's provided an essential tool for dealing with nonlinear and time-varying systems. Engineers were quick to take advantage of them to do extensive cut-and-try design work on paper instead of doing it in the development laboratory or on the test range. In many instances, particularly when designing guidance and control systems, it became clear that a more systematic approach was desirable. This led to a renewed interest in an old subject, the calculus of variations, and to the discovery of an interesting extension of this subject, dynamic programming.' The application of these techniques to deterministic, nonlinear, and timevarying systems forms the first part of this lecture. The computer also made possible rapid data-processing, sometimes almost simultaneous with the generation of the data. This stimulated a re-assessment of techniques for filtering and smoothing noisy measurements. An idea that seems to have been used by Gauss in determining orbits of the planets was rediscovered about 1960 and is now gaining wide acceptance, namely recursive maximum likelihood filtering.The increased cost of testing complicated control systems also led to a requirement for better predictions of reliability and accuracy. This requirement is strongly related to the response of the control system to random fluctuations in the environment and random errors in the measurement system. The second part of this paper is concerned with these latter topics, culminating in a discussion of the design of optimum logical structures for guid-