A novel notion of connectivity for grayscale images is introduced, defined by means of a binary connectivity assigned at image-level sets. In this framework, a grayscale image is connected if all level sets below a prespecified threshold are connected. The proposed notion is referred to as grayscale level connectivity and includes, as special cases, other well-known notions of grayscale connectivity, such as fuzzy grayscale connectivity and grayscale blobs. In contrast to those approaches, the present framework does not require all image-level sets to be connected. Moreover, a connected grayscale object may contain more than one regional maximum. Grayscale level connectivity is studied in the rigorous framework of connectivity classes. The use of grayscale level connectivity in image analysis applications, such as object extraction, image segmentation, object-based filtering, and hierarchical image representation, is discussed and illustrated.