Advanced applications for the Internet need to make use of the authorization service so that users can prove what they are allowed to do and show their privileges to perform different tasks. However, for a real scalable distributed authorization solution to work, the delegation service needs to be seriously considered. In this chapter, we first put into perspective the delegation implications, issues and concepts derived from authorization schemes proposed as solutions to the distributed authorization problem, indicating the delegation approaches that some of them take. Then, we analyze interesting federation solutions. Finally, we examine different formalisms specifically developed to support delegation services, focusing on a generalization of those approaches, the Weighted Delegation Graphs solution.