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.