As a nonlinear system analysis method different from the Lyapunov theory, contraction theory is developed mainly based on the differential geometry and fluid dynamics, providing novel aspects and tools for the system control. In this paper, we introduce some basics of the contraction theory, including the combinations of contracting systems, partial contraction theory and control contraction metrics. Then we review some applications of the contraction theory, such as analyzing system stability, tracking control, %motion planning, cooperative control, state estimation and learning control. The prospect of the future development trend of the contraction theory is presented finally.