Although the standard LCDM model fits pretty well the current experimental data, the use of a rigid cosmological constant (CC) introduces two of the greatest present-day theoretical conundrums in Physics, namely the old CC and the Cosmic Coincidence problems. In order to alleviate them, many models have been built, to wit: quintessence, modified gravity theories, etc. We have focused our research on dynamical vacuum models, in which Lambda does not remain constant. Its evolution is governed by the renormalization group equation in QFT in curved space-time.  In this presentation the phenomenological status of these models will be discussed, not only at the background level, but also taking into account the linear and non-linear perturbation effects.