  The paper provides an introductory discussion about two fundamental models of
oscillator synchronization: the (continuous-time) diffusive model, that
dominates the mathematical literature on synchronization, and the (hybrid) kick
model, that accounts for most popular examples of synchronization, but for
which only few theoretical results exist. The paper stresses fundamental
differences between the two models, such as the different contraction measures
underlying the analysis, as well as important analogies that can be drawn in
the limit of weak coupling.
