Integro-differential equations play a critical role when it comes to describing some physical and biological processes. They often arise in the study of natural phenomena in which a certain memory effect is taken into account. In this talk we discuss the important issue of existence of solutions for some classes of abstract integro-differential equations. We will make extensive use of various tools including hyperbolic semigroup techniques to establish our existence results. In order to illustrate our existence results, a few applications will be discussed.