Efforts to erect a defense against attacking missiles were considered and pushed forward from the beginning of the missile age by the superpowers. Cold War deterrence was based on massive nuclear deterrent arsenals and offensive missiles with intercontinental ranges. Ballistic Missile Defense (BMD) advocates argue that missile defense is feasible and necessary to discourage proliferation. Opponents claim that missile defenses can be easily fooled and would lead to new arms races. This chapter describes the history and development of BMD programmes, the role scientists played in these developments, and the current debate to establish BMD systems, which reflects the old arguments about invulnerability, feasibility, costs and the implications for arms control.