After more than 70 years of evolution, great achievements have been made in machine translation. Especially in recent years, translation quality has been greatly improved with the emergence of neural machine translation (NMT). In this article, we first review the history of machine translation from rule-based machine translation to example-based machine translation and statistical machine translation. We then introduce NMT in more detail, including the basic framework and the current dominant framework, Transformer, as well as multilingual translation models to deal with the data sparseness problem. In addition, we introduce cutting-edge simultaneous translation methods that achieve a balance between translation quality and latency. We then describe various products and applications of machine translation. At the end of this article, we briefly discuss challenges and future research directions in this field.