In this talk, I will briefly present the problems of maintenance in multi-robot systems. Maintenance problems arise when a group of robots, able to interact through an ad-hoc communication network or a relative sensing equipment, are tasked to perform a mission while maintaining some collective property of their interconnection. I will first quickly introduce the notion of graph and frameworks, the related matrices, the connectivity and rigidity properties. I will then show how these properties can be represented by a simple algebraic concepts such as the algebraic connectivity and the rigidity eigenvalue. Secondly I will introduce the maintenance problems and present gradient-based algorithm to solve them. I will then show the methodologies that allow those algorithms to be implemented on distributed multi-robot architectures. Thirdly I will show how additional requirements can be easily embedded in maintenance problems by the definition of suitable adjacency relations. All the methodologies will be presented with a critical approach, showing pros and cons of each choice. Finally I will conclude the talk providing some practical examples illustrating the presented methodologies.