The aim of this survey is to investigate the question of whether an analytic
dynamical system is locally conjugate to a global one. For instance,
Poincaré's and König's linearization theorems assert that complex dynamical
systems (respectively, continuous and discrete) near a stationary hyperbolic
point are locally conjugate to their linear part. Since this situation is
generic, one may wonder if *every* holomorphic dynamical system is locally
conjugate to a global one (algebraic, say) or, if that is not the case, which
kind of conditions ensure this property of "glocality" holds.