Extreme learning machine (ELM) is a new learning algorithm for the single hidden layer feedforward neural networks. Compared with the conventional neural network learning algorithm it overcomes the slow training speed and over-fitting problems. ELM is based on empirical risk minimization theory and its learning process needs only a single iteration. The algorithm avoids multiple iterations and local minimization. It has been used in various fields and applications because of better generalization ability, robustness, and controllability and fast learning rate. In this paper, we make a review of ELM latest research progress about the algorithms, theory and applications. It first analyzes the theory and the algorithm ideas of ELM, then tracking describes the latest progress of ELM in recent years, including the model and specific applications of ELM, finally points out the research and development prospects of ELM in the future.