Achieving high accuracy in automatic translation tasks has been one of the challenging goals for researchers in the area of machine translation since decades. Thus, the eagerness of exploring new possible ways to improve machine translation was always the matter for researchers in the field. Automatic translation as a key application in the natural language processing domain has developed many approaches, namely statistical machine translation and recently neural machine translation that improved largely the translation quality especially for Latin languages. They have even made it possible for the translation of some language pairs to approach human translation quality. In this paper, we present a survey of the state of the art of statistical translation, where we describe the different existing methodologies, and we overview the recent research studies while pointing out the main strengths and limitations of the different approaches.