We will discuss some recent developments on abstract Cesàro spaces, which generalizes Cesàro spaces \(Ces_p\) and \(ces_p\). In particular, duality of abstract Cesàro spaces will be presented in details, as well as their connections with down spaces. We shall look on those spaces also from the point of view of optimal range and optimal domain of Cesàro operator. Finally, results on interpolation of Cesàro spaces will be also presented. As we will see, the
proposed - very general point of view allows to grasp and exhibit the nature of the problem while proposed methods seems to simplify already known results even for \(Ces_p\) spaces. We shall also point out the big difference between Cesàro spaces on \([0,\infty)\) and on \([0,1]\).
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