Abstract: The problems of how to reduce the sampling rate in the broadband analog signal digitization and how to compress effectively the large amount of data for storage are always concerned by researchers. The recent proposed Compressive Sampling or Compressive Sensing method to solve the said problems is introduced in this paper. The method, which employs non-adaptive linear projections that preserve the structure of the signal, can capture and represent the compressible signal at a rate significantly below Nyquist rate. This paper not only presents the key procedures of this theory but also lists a variety of applications and points out the questions to be studied.