Outsourcing data to the cloud has become prevalent, so Searchable Symmetric Encryption (SSE), one of the methods for protecting outsourced data, has arisen widespread interest. Moreover, many novel technologies and theories have emerged, especially for the attacks on SSE and privacy-preserving. But most surveys related to SSE concentrate on one aspect (e.g., single keyword search, fuzzy keyword search) or lack in-depth analysis. Therefore, we revisit the existing work and conduct a comprehensive analysis and summary. We provide an overview of state-of-the-art in SSE and focus on the privacy it can protect. Generally, (1) we study the work of the past few decades and classify SSE based on query expressiveness. Meanwhile, we summarize the existing schemes and analyze their performance on efficiency, storage space, index structures, and so on.; (2) we complement the gap in the privacy of SSE and introduce in detail the attacks and the related defenses; (3) we discuss the open issues and challenges in existing schemes and future research directions. We desire that our work will help novices to grasp and understand SSE comprehensively. We expect it can inspire the SSE community to discover more crucial leakages and design more efficient and secure constructions.