There exist renormalization schemes that explicitly preserve the scale invariance of a theory at the quantum level. Imposing a scale-invariant renormalization breaks renormalizability and induces new nontrivial operators in the theory. In this work, we study the effects of such scale-invariant renormalization procedures. On the one hand, an explicitly quantum scale-invariant theory can emerge from the scale-invariant renormalization of a scale-invariant Lagrangian. On the other hand, we show how a quantum scale-invariant theory can equally emerge from a Lagrangian visibly breaking scale invariance renormalized with scale-dependent renormalization (such as the traditional (MS) over bar scheme). In this last case, scale invariance is hidden in the theory, in the sense that it only appears explicitly after renormalization.