With the rapid development of the mobile Internet a nd the Internet of Things, the number of personal wireless devices has grown exp o nentially, result ing in the increase of massive spectrum data. Therefore, the bi g spectrum data are literally formed. Meanwhile, the spect rum deficit is also increasingly precarious. Effective big spectrum data process ing is significant in improving the spectrum utilization . Firstly, fr om a perspective of wireless communication, a definition of big spectrum data is presented and its characteristics are also analyzed. Th en, p romising machine learning methods to analyze and utilize the big spectrum data are summarized, such as, the distributed and parallel learning, extreme lea rning machine, kernel b a sed learning, deep learning, reinforcement learning, game learning, and transfer learning. Finally, several open issues and research trends are addressed.