In the classical information theory, coding state can be accurately copied and distinguished; while in quantum information, it is impossible to copy, delete and distinguish non-orthogonal states due to the superposition of states. However, discrimination and cloning of quantum states have extensive applications in the new-type quantum information science such as receiving and eavesdropping in the quantum cryptography and so on. In this review paper, the mathematical concepts and the related research results about discrimination and cloning of quantum states are briefly introduced.