  It is well-known that a constant $\Lambda$-term is a traditional building
block of the concordance $\Lambda$CDM model. We show that this assumption is
not necessarily the optimal one from the phenomenological point of view. The
class of running vacuum models, with a possible running of the gravitational
coupling G, are capable to fit the overall cosmological data
SNIa+BAO+H(z)+LSS+BBN+CMB better than the $\Lambda$CDM, namely at a level of
$\sim 3\sigma$ and with Akaike and Bayesian information criteria supporting a
strong level of statistical evidence on this fact. Here we report on the
results of such analysis.

General Relativity and Quantum Cosmology