Object boundaries are generally characterized by grey level intensity transitions. In order to detect these variations, gradient masks are widely used, and this paper surveys the morphological framework of gradient operators. Morphological gradients are based on the difference between extensive and anti-extensive transformations. For instance dilations and erosions with structuring elements containing their origin belong to this class of transformations. Generally, these gradients are used in segmentation applications with edge finders such as sequential searches, thresholdings or the watershed transformation. The robustness of this latter transformation allows more tolerances for the construction of a gradient operator. After a short introduction to gradients in digital images the gradients available in mathematical morphology are presented: Beucher, internal and external, thick, regularized, directional, and thinning/thickening gradients. Applicability and performance of each gradient are briefly evaluated, followed by a generalization of the morphological framework of gradient operators to other digital sources.