In this chapter, we provide an overview of several related problems in which we can apply the techniques developed in Chapters 2–6. We first study the least gradient problem, that is, the problem of minimisation of total variation with respect to a given Dirichlet boundary condition. We discuss several possible formulations of this problem in a metric measure setting, and in regular bounded open subsets of a metric measure space, we describe the relation between the least gradient problem and the Dirichlet problem for the 1-Laplacian operator. Section 7.2 deals with the Cheeger problem and the Cheeger cut problem in the general framework of metric measure spaces. Our first goal is to study the problem of characterising the Cheeger constant of a bounded domain and the identification of the Cheeger sets. Furthermore, we prove a version of the Max-Flow Min-Cut Theorem. Then, we consider the Cheeger cut problem of partitioning the space into two parts so that the Cheeger constant of the whole space is achieved, and as a consequence, we obtain a Cheeger inequality along the lines of the classical one for Riemannian manifolds obtained by Cheeger in 1970.