With the development of information technology, especially the wide application of Internet-involved products, a large number of areas require real-time processing of massive and high velocity data. How to learn informative knowledge from ″data ocean″ becomes increasingly important. Traditional batched machine learning algorithms come to be pale when dealing with big data. However, the online learning framework employs streaming computing mode and deals with the data directly in the memory, which provides a promising tool for the learning of big data. This online learning framework has a bright prospect in facing difficulties and challenges when learning big data. This paper concludes the traditional and state-of-the-art online learning algorithms, the main contents include: (1) online linear learning algorithms; (2) online kernel learning algorithms; (3) other classical online learning algorithms; (4) optimization methods of online learning algorithms. Additionally, the implementation of online framework on deep learning models is then introduced to inspire interested researchers. Eventually, this paper discusses the key issues and some applications of online learning algorithms, which is followed by the research directions of the research direction.