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Emergence is a word that plays a central role in the natural or manifest image of the world, within which we organize our ordinary knowledge. Even though some interpretations of the "scientific image" leave no place for emergence, sciences increasingly made use of this word. But many philosophical arguments have been made against the consistence or validity of this concept. This chapter presents a computational view of emergence, alternative to the usual combinatorial view common among philosophers, that is formulated in terms of parts and wholes. It shows that computational emergence can be characterized in terms of causation, and that a subclass of computationally emergent processes displays many of the connotations of the scientific use of the term. After having so captured a concept of emergence, I turn to the question of applying the concept and testing whether some instantiations exist.

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