Program invariants are important properties of software, which play important roles in many software research fields, such as verification, debugging, and testing. Since the end of 20th century, research on dynamic analysis based program invariant synthesis has become a hot topic in related research areas and made remarkable progress. This paper collects 90 related papers to survey researches within this topic. To dynamically synthesize invariants is the key problem of this field. An abstract framework, “learner-oracle”, is proposed to model and subsume synthesis approaches. In general, the synthesis approaches can be classified into four types, i.e. pattern enumeration based approaches, numerical calculation based approaches, statistical learning based approaches, and symbolic execution based approaches. Furthermore, important applications are discussed of dynamic invariants in software engineering and software verification. Then, important subject programs and synthesis tools are briefly summarized. Finally, the remaining opportunities are presented and a conclusion is reached.