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In this article, the author explores the notion of Collective Intelligence CI as an emerging computing paradigm. The article is meant to provide a historical and contextual view of CI through the lenses of as many related disciplines as possible biology, sociology, natural and environmental sciences, physics in conjunction with the computer science point of view. During this explorative journey, the article also aims at pinpointing the current strengths and weaknesses of CI-related computational and system engineering design and implementation methodologies of CI-based systems. A non-exhaustive list of case studies set up the stage for CI applications as well as challenging research questions. These can be particularly directed towards the Social Web, as a very prominent example of synergistic interactions of a group of people with diverse cultural and professional backgrounds and its potential to become a platform for the emergence of truly CI-based systems.