The transportation planning process is considered a point of interest in the field of urban sustainable development. After many years of development and knowledge, it was found that transportation modelling has a fundamental role in transportation planning. There are many types of transportation models that represent the travel behavior in the study area. The traditional travel demand model is one of the most widely used in transportation planning modelling. Mainly there are four stages in the traditional travel demand model. These stages are trip generation, trip distribution, mode choice, and trip assignment. The trip assignment model is the result for the previous three stages and could estimate the traffic flow on network links. This paper represents the traditional travel demand model so-called "four-step model" and its structure as well as the validation methods for the trip assignment model. The overview also includes the applications of the traffic assignment model, considering it the final stage of the travel demand model, in the sustainable development of urban cities.