Multiple Criteria Decision Aiding (MCDA) is a domain of Operations Research and Management Science mainly devoted to the development of methods, techniques and tools aiming to help decision makers in complex decision processes. This paper describes DecSpace, a framework to explore a wide range of methods of that kind. DecSpace is a web-based framework, making it possible to explore solutions for problems involving one or more methods. Persistent workspaces also make it possible to reuse solutions. In this sense, DecSpace is intended for use in teaching and researching in MCDA methods, as well for professional use as a Decision Support System for engineering and management scenarios where decisions based on those methods are to be considered. DecSpace has an open architecture, making it possible to use methods implemented locally, fully integrated as part of the local application, or methods available from remote servers, if exposed as web services.