With the rapid development from traditional machine learning (ML) to deep learning (DL) and reinforcement learning (RL), dialog system equipped with learning mechanism has become the most effective solution to address human-machine interaction problems. The purpose of this article is to provide a comprehensive survey on learning-based human-machine dialog systems with a focus on the various dialog models. More specifically, we first introduce the fundamental process of establishing a dialog model. Second, we examine the features and classifications of the system dialog model, expound some representative models, and also compare the advantages and disadvantages of different dialog models. Third, we comb the commonly used database and evaluation metrics of the dialog model. Furthermore, the evaluation metrics of these dialog models are analyzed in detail. Finally, we briefly analyze the existing issues and point out the potential future direction on the human-machine dialog systems.