The relationship between quantum state control and matrix decomposition is reviewed. The matrix decomposition newly applied in quantum information science,i.e. Cartan decomposition based on group theory and cosine-sine decomposition based on numerical linear algebra,is introduced firstly. Then the current research situation and the results in this area are reviewed. These results play important roles in quantum entanglement dynamics,the control of quantum states and optimization of quantum circuit.Finally,the Cartan decomposition of a 2-qutrit logic gate is given.