Nowadays, information sharing as an indispensable part appears in our vision, bringing about a mass of discussions about methods and techniques of privacy preserving data publishing which are regarded as strong guarantee to avoid information disclosure and protect individuals' privacy. Recent work focuses on proposing different anonymity algorithms for varying data publishing scenarios to satisfy privacy requirements, and keep data utility at the same time. K-anonymity has been proposed for privacy preserving data publishing, which can prevent linkage attacks by the means of anonymity operation, such as generalization and suppression. Numerous anonymity algorithms have been utilized for achieving k-anonymity. This paper provides an overview of the development of privacy preserving data publishing, which is restricted to the scope of anonymity algorithms using generalization and suppression. The privacy preserving models for attack is introduced at first. An overview of several anonymity operations follow behind. The most important part is the coverage of anonymity algorithms and information metric which is essential ingredient of algorithms. The conclusion and perspective are proposed finally.