The innovations diffusion is a process of communication by which a new idea spreads among a population. A successful propagating leads researchers to seek the elements, which approve and consequently contribute to its spread, or otherwise, find the elements that prevent it. In fact, many efforts were made to models this social phenomenon; however, each one had its strengths and weaknesses. Therefore, this paper aims (1) to discuss and to analyze existing models showing their utility and limitation, (2) highlighting the detail of their applications, and (3) suggesting a taxonomy, which resumes the state of art. Then, to address the current social networks models, it seems necessary to begin by presenting the diffusion of innovation theory, then to detail models, which do not incorporate the social structure, more precisely the mathematical models.