For intercept or rendezvous of a nonmaneuvering target, application of modern control theory leads naturally to the guidance policy called predictive guidance. The paper reviews the theory of predictive guidance and presents the results in a more complete form than was previously available. A new method of implementing predictive guidance, called multipoint guidance, is presented. In the context of command guidance for intercepting a ballistic re-entry vehicle, multipoint guidance has been found to yield miss-distances similar to those of a standard implementation of predictive guidance while requiring much less real-time data processing.