We describe some slow-entropy-type notions classifying dynamical systems up to isomorphism ; one is the {\bf symbolic complexity} which counts the number of words in the language of a symbolic system, and provides an invariant for topological isomorphism ; another is the {\bf measure-theoretic complexity}, which is a natural modification of the symbolic complexity and is invariant under measure-theoretic isomorphism. In both cases, when the complexity has a simple form, the system is fully known: when the symbolic complexity is sub-linear, the system is generated by a finite number of substitutions, and, when the measure-theoretic complexity is bounded, the system is a translation of a compact group.