Important notions in control theory are related with the properties of some subsets of the state space, the output space, or the input space of the system. Such subsets are the domains of attraction of an equilibrium, the admissible sets of state or control variables in the case of constrained control problems or the invariant sets where the trajectories of the system are confined. In most applications, these regions are connected subsets of the state or the input space. The aim of this chapter is to introduce two types of representation of connected sets and to recall their basic properties that are essential for the development of comparison methods. Special attention is paid to the approaches of enlargement and size reduction of these sets.