If a and b are two integers, with b non zero, then there are two integers q and r such that a = bq + r, and |r| < |b|. This so-called Euclidean division property plays a fundamental role in the arithmetic of the usual integers. Other kinds of numbers, that one could call generalized integers, also turn out to be important. The aim of this talk is to present some properties of these numbers, and to study questions related to the Euclidean division.