In this talk, we are going to survey the basic elements of temporal logics based on intervals instead of points. We shall first give the most fundamental
definitions, with particular attention to the parameters that influence the computational properties of logics of time intervals. Then, we shall see
the most important results that we have obtained in the past years. Finally, we shall focus our attention on the currently open problems, and, in particular,
those on which we are working on in joint with the University of Malaga. We shall conclude by proposing interesting line of research closely connected
to such problems.