We cannot analyze big data, which attracts recent attentions in industry and academy, by batch processing algorithms developed in data mining because big data, by definition, cannot be uploaded and processed in the memory of a single system. So an imminent issue is to develop various leaning algorithms so that they can be applied to big data. In this paper, we review various algorithms for support vector machines in the literature. Particularly, we introduce online type and parallel processing algorithms that are expected to be useful in big data classifications and compare the strengths, the weaknesses and the performances of those algorithms through simulations for linear classification.