ABSTRACT
This chapter presents a paper which is a slightly expanded version of the talk the author gave at the conference "Geometria e Variabile Complessa a Bologna", held in Bologna in the February 1989, in the occasion of the celebrations for the 900th year from the foundation of that University. It focuses on a particular, but relevant, aspect of Federigo Enriques' investigations, namely the study of canonical and pluricanonical images of curves and surfaces. The idea is to make a hystorical reconstruction of the contribution of Enriques and his school on this subject, but also to mention some of the main more recent developements. Enriques’ papers are still an incredible source of problems. The chapter makes some comments on one problem, often explicitely posed by Enriques: the study and classification of irregular surfaces of general type (which have been also the object of Catanese's talk).
