Leibniz did write ``the Leibniz rule'', and Jean-Louis Loday defined ``Leibniz algebras'' and their cohomology. But the definition of the corresponding objects in the realm of Lie algebroids and Lie-Rinehart algebras has been approached differently by different authors.

We shall outline the problem, explain solutions and describe two of the main examples, generalized tangent bundles and, more generally, Courant algebroids. We shall describe the extension of the derived bracket approach from the case of Lie algebroids to that of Loday algebroids (following Grabowski-Khudaverdian-Poncin).