We study a generic class of time-evolving vacuum models which can provide a better phenomenological account of the overall cosmological observations as compared to the Λ cold dark matter (ΛCDM). Among these models, the running vacuum model (RVM) appears to be the most motivated and favoured one, at a confidence level of ∼3σ. We further support these results by computing the Akaike and Bayesian information criteria. Our analysis also shows that we can extract fair signals of dynamical dark energy (DDE) by confronting the same set of data to the generic XCDM and CPL parametrizations. In all cases we confirm that the combined triad of modern observations on baryonic acoustic oscillations, large-scale structure formation, and the cosmic microwave background, provide the bulk of the signal sustaining a possible vacuum dynamics. In the absence of any of these three crucial data sources, the DDE signal cannot be perceived at a significant confidence level. Its possible existence could be a cure for some of the tensions existing in the ΛCDM when confronted to observations.