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Emergence is usually associated with the appearance of novel and unexpected behavior at larger length scales than those characterizing the “microscopic/fundamental” systems under scrutiny. Standard examples include the collective behavior of a large number of building blocks (particles like electrons, molecules, people, etc.) or special limiting behavior such as critical points (traffic jams, epidemics, economic collapse, phase transitions etc.).  Emergence is ubiquitous through science and acts as a mediator between different scientific disciplines, linking for instance physics and chemistry, chemistry and biology or mathematics and social behavior. The science of emergence consists of understanding such connections and is usually demarcated by universal principles that hold for large classes of collective behavior such as symmetry-breaking patterns, self-organization, (quantum) phase transitions and (quantum) critical behavior. Similar phenomena also appear in applications to new quantum & programmable materials, big data, cognition, and urban issues. Emergence leads to fundamental, mathematical and philosophical questions, such as how to bridge from one scale to the next.