This paper aims to survey various techniques utilized for content moderation in end-to-end encryption systems. We assess the challenging aspect of content moderation: maintaining a safe platform while assuring user privacy. We study the unique features of some content moderation techniques, such as message franking and perceptual hashing, and highlight their limitations. Currently implemented content moderation techniques violate the goals of end-to-end encrypted messaging to some extent. This has led researchers to develop remediations and design new security primitives to make content moderation compatible with end-to-end encryption systems. We detail these developments, analyze the proposed research efforts, assess their security guarantees, correlate them with other proposed solutions, and determine suitable improvements under specific scenarios.