This paper describes some of the most recent algorithmic techniques of mathematical morphology. The classical parallel and sequential methods mostly involve numerous scannings of all the image pixels and are thus inefficient on conventional computers. To get rid of this drawback, the key idea is to consider, at each step, only the pixels whose value may be modified. Two classes of algorithms rely on this principle: the first one realizes an encoding of the object boundaries as loops which are then propagated in the image. The second one embraces the algorithms based on breadth- first image scanning enabled by queues of pixels. The algorithms belonging to these two families are extremely efficient and particularly suited to nonspecialized equipments, since they require random access to the pixels. Moreover, the 'customized' image scannings they are based on allow one to develop more accurate and flexible procedures: for example algorithms for computing exact Euclidean distance functions have been derived from the first class. On the other hand, the queue-based algorithms work in any kind of grid, in the Euclidean and geodesic cases, and extend to any dimension and even to graphs.