As an important research topic in social media text sentiment analysis, cross-domain text sentiment classification aims to use the source domain resources or model transfer to serve the target domain text sentiment classification task, which can effectively solve the problem of insufficient data marking in specific domains. In order to solve the problem of cross-domain sentiment adaptation, this article summarizes the existing studies of cross-domain sentiment classification from three perspectives, i.e., (1) it can be divided into transductive and inductive cross-domain sentiment classification methods according to whether there is labeled data in the target domain; (2) it can be divided into instance transferring based, feature transferring based, model or parameters transferring based, sentiment dictionary based, joint sentiment topic based, and graph model based methods according to different sentiment adaption strategies; (3) it can also be divided into single-source domain and multi-source domains of cross-domain sentiment classification according to the number of available source domains. In addition, it is also introduced that a new approach of deep transfer learning to solve cross-domain sentiment classification problems, and summarize its latest research results in cross-domain sentiment classification. Finally, the challenges are combined with key issues of current cross-domain sentiment classification technology and further study directions are pointed out.