Important unsteady fluid dynamic effects occur in a wide range of modern engineering problems. A review and critical appraisal has been made of the current research activities on topics that contain essential and unique unsteady features, especially those which cannot be approximated by quasi-steady analyses. A synopsis of the main areas covered in this paper is given below. Linear potential theory is well advanced and most of the fundamental concepts are well understood. The theory has been specially adapted for engineering purposes to many complex geometries and flow environments, but its limitations are not well established in most cases. Transonic flows have received considerable attention in recent years, and the profusion of numerical analyses of nonlinear unsteady flows has outstripped measurements. However, new experimental investigations are underway. Numerical codes are becoming much more efficient, and efforts are being made to incorporate viscous effects into them. Unsteady boundary layers have been computed with almost no complementary experimental guidance, and this deficiency is particularly acute in the turbulent case. A major conceptual difference between steady and unsteady separation has been identified and is continuing to be studied. Unsteady stall is currently under detailed examination, and recent experiments have shed considerable new insight on the fundamental mechanisms of dynamic stall on oscillating airfoils. New attempts to treat unsteady stall as a strong viscous-inviscid interaction problem are needed. Vortex shedding from bluff bodies is difficult to predict, especially in cases where body oscillations are self-induced by the fluctuating fluid dynamic forces. Nonlinear oscillator models are limited by a lack of understanding of the basic fluid dynamic phenomena. The trailing edge condition of Kutta and Joukowski for thin airfoils has been called into question recently for unsteady flows at high frequencies or with trailing-edge separation. The correct modeling of this condition is important in predicting the fluid dynamic forces on all thin lifting surfaces that fluctuate. Considerable progress has been made in each of these subjects, but none of them has been mastered. The questions that remain unanswered pose intriguing challenges to the fluid dynamics community.