A variety of continuous-time differential functions have been developed to investigate dynamic advertising problems in business and economics fields. Since major dynamic models appearing before 1995 have been reviewed by a few survey papers, we provide a comprehensive review of the dynamic advertising models published after 1995, which are classified into six categories: (i) Nerlove-Arrow model and its extensions, (ii) Vidale-Wolfe model and its extensions, (iii) Lanchester model and its extensions, (iv) the diffusion models, (v) dynamic advertising-competition models with other attributes, and (vi) empirical studies for dynamic advertising problems. For each category, we first briefly summarize major relevant before-1995 models, and then discuss major after-1995 models in details. We find that the dynamic models reviewed in this paper have been extensively used to analyze various advertising problems in the monopoly, duopoly, oligopoly, and supply chain systems. Our review reveals that the diffusion models have not been used to analyze advertising problems in supply chain operations, which may be a research direction in the future. Moreover, we learn from our review that very few publications regarding dynamic advertising problems have considered the supply chain competition. We also find that very few researchers have used the diffusion model to investigate the dynamic advertising problems with product quality as a decision variable; and, the pricing decision has not been incorporated into any extant Lanchester model. The paper ends with a summary of our review and suggestions on possible research directions in the future.