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We discuss the concept of emergence, and try to show that it is one of the most significant issues in the study of complex living systems. We stress particularly that emergent properties possess a specific causal power, which is not reducible to the power of their constituents. The emergence of physiological functions is profoundly related to the self-organized dynamics of biological systems. The increasing complexity of cellular and organismal activity favors the emergence of novelties and the integration of the active parts into an autonomous whole.