1 Introduction

2 Prerequisites
2.1 Quantum states
2.2 Quantum measurements
2.3 Quantum control models

3 Controllability and open-loop control of quantum systems
3.1 Controllability
3.2 Optimal control
3.3 Lyapunov-based control design
3.4 Variable structure control
3.5 Incoherent control

4 Some results on closed-loop design methods
4.1 Closed-loop learning control
4.2 Quantum feedback control

5 Conclusions and perspectives