  Ward-Takahashi identities are nonperturbative relations between correlation
functions and arising from symmetries in quantum and statistical fields
theories, as Noether currents conservation for classical theories. Since their
historical origin, these identities were considered to prove the exact relation
between counter-terms to all order of the perturbative expansion. Recently they
have been considered in relation with nonperturbative renormalization group
aspects for some classes of quantum field theories namely tensorial group field
theories and matrix models, both characterized by a specific non-locality in
their interactions, and expected to provide discrete models for quantum
gravity. In this review, we summarize the state of the art, focusing on the
conceptual aspects rather than technical subtleties, and provide a unified
reflection on this novel and promising way of investigation. We attached great
importance to the pedagogy and the self-consistency of the presentation.
