The recent discovery of gravitational-wave burst GW150914 marks the coming of a new era of gravitational-wave astronomy, which provides a new window to study the physics of strong gravitational field, extremely massive stars, extremely high energy processes, and extremely early universe. In this article, we introduce the basic characters of gravitational waves in the Einstein's general relativity, their observational effects and main generation mechanisms, including the rotation of neutron stars, evolution of binary systems, and spontaneous generation in the inflation universe. Different sources produce the gravitational waves at quite different frequencies, which can be detected by different methods. In the lowest frequency range (f < 10 −15 Hz), the detection is mainly dependent of the observation of B-mode polarization of cosmic microwave background radiation. In the middle frequency range (10 −9 < f < 10 −6 Hz), the gravitational waves are detected by analyzing the timing residuals of millisecond pulsars. And in the high frequency range (10 − 4 < f < 10 4 Hz), they can be detected by the space-based and ground-based laser interferometers. In particular, we focus on the main features, detection methods, detection status, and the future prospects for several important sources, including the continuous sources (e.g., the spinning neutron stars, and stable binary systems), the burst sources (e.g., the supernovae, and the merge of binary system), and the stochastic backgrounds generated by the astrophysical and cosmological process. In addition, we forecast the potential breakthroughs in gravitational-wave astronomy in the near future, and the Chinese projects which might involve in these discoveries.