This paper introduces the concepts of distributed intelligence, outlining the motivations for studying this field of research. We then classify common systems of distributed intelligence based upon the types of interactions exhibited, since the type of interaction has relevance to the solution paradigm to be used. We outline three common paradigms for distributed intelligence --- the bioinspired paradigm, the organizational and social paradigm, and the knowledge-based, ontological paradigm --- and give examples of how these paradigms can be used in multi-robot systems. We then look at a common problem in multi-robot systems --- that of task allocation --- and show how the solution approach to this problem is very different depending upon the paradigm chosen for abstracting the problem. Our conclusion is that the paradigms are not interchangeable, but rather the selection of the appropriate paradigm is dependent upon the specific constraints and requirements of the application of interest. Further work is needed to provide guidance to the system designer on selecting the proper abstraction, or paradigm, for a given problem.