Mathematical models are important tools in a holistic representation of the important components of a logistics and supply chain system, and in formulating logistics and supply chain policies to address the underlying issues and choices. To examine the issues surrounding a logistics and supply chain system, an understanding of the integrated mathematical models of the system can be very useful. A critical review of the integrated mathematical models of the logistics and supply chain system (integrating the logistics sector in the economy-wide models) is missing in the existing literature. The objective of this paper is to discuss the existing economy-wide logistics and supply chain models (mathematical and computational methods), which can be used for the formulation of logistics and supply chain systems and policies or project planning. These models include general equilibrium models, input-output analysis, and optimal control models, among others. The future directions in research in modeling in this area are also stated. As a critical discussion of the modelling and computational methods in integrated economic and logistics and supply chain systems is lacking in the existing literature, this paper makes an original contribution.