  When a large number of similar entities interact among each other and with
their environment at a low scale, unexpected outcomes at higher spatio-temporal
scales might spontaneously arise. This nontrivial phenomenon, known as
emergence, characterizes a broad range of distinct complex systems -- from
physical to biological and social ones -- and is often related to collective
behavior. It is ubiquitous, from non-living entities such as oscillators that
under specific conditions synchronize, to living ones, such as birds flocking
or fish schooling. Despite the ample phenomenological evidence of the existence
of systems' emergent properties, central theoretical questions to the study of
emergence remain still unanswered, such as the lack of a widely accepted,
rigorous definition of the phenomenon or the identification of the essential
physical conditions that favour emergence. We offer here a general overview of
the phenomenon of emergence and sketch current and future challenges on the
topic. Our short review also serves as an introduction to the Theme Issue
"Emergent phenomena in complex physical and socio-technical systems: from cells
to societies", where we provide a synthesis of the contents tackled in the
Issue and outline how they relate to these challenges, spanning from current
advances in our understanding on the origin of life to the large-scale
propagation of infectious diseases.
