Abstract: In the traditional signal sampling process, Shannon theorem must be satisfied for preventing signal distortion. But in some practical applications (such as image and video processing systems), an increased sampling frequency will substantially increase the data storage and transmission costs. Different from the traditional signal acquisition process, compressive sensing, which is a new theory that captures and represents compressible signals at a sampling rate significantly below the Nyquist rate. It first employs nonadaptive linear projections that preserve the structure of the signal, and then the signal reconstruction is conducted using an optimization process from these projections. Compressive sensing has broad applications such as compressive imaging, analog-to-information conversion, biosensing, etc. This paper surveys the principles of compressive sensing and its related applications. Some further work on this theory is also presented.