The explosive popularity of microblogging services encourages more and more online users to share their opinions, and sentiment analysis on such opinion-rich resources has been proven to be an effective way to understand public opinions. On the one hand, the brevity and informality of microblogging data plus its wide variety and rapid evolution of language in microblogging pose new challenges to the vast majority of existing methods. On the other hand, microblogging texts contain various types of emotional signals strongly associated with their sentiment polarity, which brings about new opportunities for sentiment analysis. In this paper, we investigate propagation-based sentiment analysis for microblogging data. In particular, we provide a propagating process to incorporate various types of emotional signals in microblogging data into a coherent model, and propose a novel sentiment analysis framework PSA which learns from both labeled and unlabeled data by iteratively alternating a propagating process and a fitting process. We conduct experiments on real-world microblogging datasets, and the results demonstrate the effectiveness of the proposed framework. Further experiments are conducted to probe the working of the key components of the proposed framework.