  A particle system is said to be non-exchangeable if two particles cannot be
exchanged without modifying the overall dynamics. Because of this property, the
classical mean-field approach fails to provide a limit equation when the number
of particles tends to infinity. In this review, we present novel approaches for
the large-population limit of non-exchangeable particle systems, based on the
idea of keeping track of the identities of the particles. These can be
classified in two categories. The non-exchangeable mean-field limit describes
the evolution of the particle density on the product space of particle
positions and labels. Instead, the continuum limit allows to obtain an equation
for the evolution of each particle's position as a function of its (continuous)
label. We expose each of these approaches in the frameworks of static and
adaptive networks.
