In the current large-scale data retrieval tasks, learning to hash methods can learn compact binary codes, which saves storage space and can quickly calculate the similarity in Hamming space. Therefore, for approximate nearest neighbor search, hashing methods are often used to improve the mechanism of fast nearest neighbor search. In most current hashing methods, the offline learning models are used for batch training, which cannot adapt to possible data changes appeared in the environment of large-scale streaming data, resulting in reduction of retrieval efficiency. Therefore, the adaptive hash functions were proposed and learnt in online hashing methods, which realize the continuous learning in the process of inputting data and make the methods can be applied to similarity retrieval in real-time. Firstly, the basic principles of learning to hash and the inherent requirements to realize online hashing were explained. Secondly, the different learning methods of online hashing were introduced from the perspectives such as the reading method, learning mode, and model update method of streaming data under online conditions. Thirdly, the online learning algorithms were further divided into six categories, that is, categories based on passive-aggressive algorithms, matrix factorization technology, unsupervised clustering, similarity supervision, mutual information measurement, codebook supervision respectively. And the advantages, disadvantages and characteristics of these algorithms were analyzed. Finally, the development directions of online hashing were summarized and discussed.