The unprecedented proliferation of mobile smart devices has propelled a promising computing paradigm, Mobile Crowd Sensing (MCS), where people share surrounding insight or personal data with others. As a fast, easy, and cost-effective way to address large-scale societal problems, MCS is widely applied into many fields, e.g., environment monitoring, map construction, public safety, etc. Despite the popularity, the risk of sensitive information disclosure in MCS poses a serious threat to the participants and limits its further development in privacy-sensitive fields. Thus, the research on privacy protection in MCS becomes important and urgent. This paper targets the privacy issues of MCS and conducts a comprehensive literature research on it by providing a thorough survey. We first introduce a typical system structure of MCS, summarize its characteristics, propose essential requirements on privacy on the basis of a threat model. Then, we survey existing solutions on privacy protection and evaluate their performances by employing the proposed requirements. In essence, we classify the privacy protection schemes into four categories with regard to identity privacy, data privacy, attribute privacy, and task privacy. Besides, we review the achievements on privacy-preserving incentives in MCS from four viewpoints of incentive measures: credit incentive, auction incentive, currency incentive, and reputation incentive. Finally, we point out some open issues and propose future research directions based on the findings from our survey.