Historical background -- Ordinary minimum problems : from the beginning of calculus to Kuhn-Tucker -- Calculus of variations : from Bernoulli to Bliss -- Minimum principle of Pontryagin and Hestenes -- Application of the Jacobi test in optimal control and neighboring extremals -- Numerical techniques for the optimal control problem -- Singular perturbation technique and its application to air-to-space interception -- Application to aircraft performance : Rutowski and Kaiser's techniques and more -- Application to rocket performance : the Goddard problem -- Application to missile guidance : proportional navigation -- Application to time-optimal rotational maneuvers of flexible spacecraft.