Large flexible spacecraft are required for several planned space missions. A proposal that active feedback control be employed to reduce the effects of structural bending and vibration in such spacecraft has provided a significant practical challenge to the theory of control of distributed parameter systems, and particularly hyperbolic systems. This limited survey provides an assessment of the contributions of this theory toward the general solution of problems in active control of flexible spacecraft, and elucidates open questions which still require further research. The development of a useful design methodology is found to require a close interplay between control theory and related areas such as modelling, aggregation, and sensor—actuator selection.