The notion of public key encryption with keyword search (PEKS) provides a flexible and efficient approach to retrieve encrypted data stored in a remote server. A main threat in PEKS is the keyword guessing attack, where disclosed keywords leak the associated data and the user’s interest. This gives rise to that the keyword privacy becomes a concern in searchable encryption. In this paper, we present a brief history of keyword privacy in searchable encryption. We make a systematic investigation of keyword privacy issue in public key-based searchable encryption. We describe keyword guessing attacks in a general PEKS scheme. According to different attackers, we refine inherent reasons and summarize enhancement achievements. This preserves the keyword privacy and provides guidance for the secure development of searchable encryption.