Grammatical Inference (GI) is a problem of inductive learning of formal languages, which deals with how to obtain the grammatical description of a formal language from given finite data drawn from the language. In this paper, the authors provide a survey of the history and recent advances in GI field. They first present some learning models for GI. Then, they enumerate methods for GI with an emphasis on the results concerning the inference of context free grammar class and its some subclasses, hidden Markov models, and stochastic context-free grammar class. At last, they briefly give some applications of GI as well as the future directions of GI research.