Emergence is one of the most fascinating and challenging aspects of complex systems, being also a controversial topic featuring long-standing debates and disagreements. In this talk I’ll discuss the benefits of formal approaches to conceptualise emergence. In doing this, I’ll argue towards a pragmatic and pluralistic stance towards emergence, which embraces multiple views while focusing on methods to establish falsifiable hypotheses and procedures to verify them. This approach will be illustrated by exploring two distinct but complementary operationalisations of emergence: (i) self-contained levels of description, related to the separation of scales, and (ii) synergistic interactions between constituents, related to interactions between scales. These approaches will be illustrated on paradigmatic models from statistical physics and computational neuroscience, and also on practical applications.