AbstractFleet management represents a relevant activity at tactical and operational levels to be faced by private companies and public agencies devoted to passengers and freight transportation services. Mathematical models and computation techniques have been developed for optimizing and simulating the operation of transport fleets in order to serve the customers demand with the objective of cost efficiency. Many fleet management problems correspond to combinatorial optimization problems, such as vehicle routing and scheduling, that are notoriously difficult to solve, even in a static context. Moreover, dynamic fleet management concern real-time requirements of the provided service and the control of unforeseen events that could affect the performances of the transport operations. The aim of this paper is to identify the most relevant problems in fleet management relatively to different transport modes, each one with specific characteristics, and to present an overview of recent contributions both in the development of mathematical models and in the design of computation algorithms.