Abstract An extensive literature review on the modelling of the linear viscoelastic (LVE) rheological properties of bitumen over the last six decades is presented in this paper. The use of reliable models can, in general, be considered as a valuable alternative tool for estimating the LVE rheological properties of bitumen. These properties are normally presented in terms of complex modulus and phase angle master curves at a particular reference temperature. The review in this paper consists of three nonlinear multivariable models, 13 empirical algebraic equations and four mechanical element approaches. The details as well as the advantages and disadvantages of the models are discussed. In general, all the models are able to predict the LVE rheological properties of unmodified bitumen as well as follow the time–temperature superposition principle (TTSP). However, the observations suggest a lack of agreement between predicted and experimental LVE rheological properties for materials that contain a phase transition, such as found for highly crystalline bitumen, structured bitumen with high asphaltenes content and highly modified bitumen.