The transportation problem is the most important and successful application of linear programming studied in the area of operations research. In the past few decades, new approaches have been developed to improve the components of the existing platform. This paper presents recent advances on reliable methods for solving transportation problem and fuzzy transportation problem through a survey table in which our comments as a remark has been included. An attempt has been made to provide a variety of methods to solve the transportation problem within a limited structure; through which ideas could be developed for designing new algorithms. It provides a better platform for further research work in the area of transportation problem.