In recent years, Intelligent Transportation Systems (ITS) have seen efficient and faster development by implementing deep learning techniques in problem domains which were previously addressed using analytical or statistical solutions and also in some areas that were untouched. These improvements have facilitated traffic management and traffic planning, increased safety and security in transit roads, decreased costs of maintenance, optimized public transportation and ride-sharing company's performance, and advanced driver-less vehicle development to a new stage. This papers primary objective was to provide a review and comprehensive insight into the applications of deep learning models on intelligent transportation systems accompanied by presenting the progress of ITS research due to deep learning. First, different techniques of deep learning and their state-of-the-art are discussed, followed by an in-depth analysis and explanation of the current applications of these techniques in transportation systems. This enumeration of deep learning on ITS highlights its significance in the domain. The applications are furthermore categorized based on the gap they are trying to address. Finally, different embedded systems for deployment of these techniques are investigated and their advantages and weaknesses over each other are discussed. Based on this systematic review, credible benefits of deep learning models on ITS are demonstrated and directions for future research are discussed.