Infrastructure management plays an important role in sustainable development and is essential for the evaluation of the socioeconomic feasibility of existing projects and the development of new ones. This paper presents a review of key aspects involved in the maintenance and operation of infrastructure under uncertainty. It discusses the main conceptual and theoretical principles and guides the reader through different aspects of the problem by offering a large set of state-of-the-art references. Although the paper does not provide a comprehensive description of all maintenance methods and policies available in the literature, it critically reviews the main approaches. The concepts presented and discussed in this paper provide the basis to build models that can be used for making better decisions for maintaining and operating infrastructure systems.