ABSTRACT: Connected operators enlarge the flat zones of an image and never create a contour where no contour was present. This definition is too vague to be useful in practice, except for binary images. For grey-tone images a more precise characterization has to be given in order to be operational. This leads to the introduction of floodings, razings, flattenings and levelings. Extending the notion of a flat zone and of a contour leads to extended connected operators. The chapter concludes by showing the versatility and power of these operators in practice.