The modelling of dynamic system is a challenging problem in a large number of applications like prediction, bio-data modelling, computer vision or time-series processing. To face the complexity and the non-linearity of data, new models are regularly proposed through the literature. Among proposed models artificial neural network (ANN) have benefit of a large interest in the scientist community. The use of latent variables to extract and diffuse complex features in multilayer feedforward neural networks provide usually excellent results. In 1982, Hopfield proposes a generative and deterministic neural network to model a physical system. His work leads to the emergence of a large number of generative neural networks: Boltzmann Machine and its extensions. Different applications lead researchers to propose new extensions for the Boltzmann machine to handle dynamic systems, continuous variables or systems with complex features. In parallel, a new model named the Diffusion Network has emerged, also inspired from Hopfield network but with continuous stochastic properties and designed to solve stochastic differential equations. This paper has the objective to review the evolution of the Boltzmann Machine's family with a synthetic and historical vision and their development for dynamic problem. To write this review, we selected articles from journals/conferences and review articles (1/3 are <7 years) quoted in meta sources (Scopus and Web-of-Sciences). Once a clearly research question was asked – How generative networks model dynamic systems ? – we defined our search terms for papers. Note that not all extensions to Boltzmann machines are presented in this paper. Only models related with dynamic applications and most salient models were retained.