  Next year we will celebrate 100 years of the cosmological term, $\Lambda$, in
Einstein's gravitational field equations, also 50 years since the cosmological
constant problem was first formulated by Zeldovich, and almost about two
decades of the observational evidence that a non-vanishing, positive,
$\Lambda$-term could be the simplest phenomenological explanation for the
observed acceleration of the Universe. This mixed state of affairs already
shows that we do no currently understand the theoretical nature of $\Lambda$.
In particular, we are still facing the crucial question whether $\Lambda$ is
truly a fundamental constant or a mildly evolving dynamical variable. At this
point the matter should be settled once more empirically and, amazingly enough,
the wealth of observational data at our disposal can presently shed true light
on it. In this short review I summarize the situation of some of these studies.
It turns out that the $\Lambda=$const. hypothesis, despite being the simplest,
may well not be the most favored one when we put it in hard-fought competition
with specific dynamical models of the vacuum energy. Recently it has been shown
that the overall fit to the cosmological observables
$SNIa+BAO+H(z)+LSS+BBN+CMB$ do favor the class of "running" vacuum models
(RVM's) -- in which $\Lambda=\Lambda(H)$ is a function of the Hubble rate --
against the "concordance" $\Lambda$CDM model. The support is at an
unprecedented level of $\sim4\sigma$ and is backed up with Akaike and Bayesian
criteria leading to compelling evidence in favor of the RVM option and other
related dynamical vacuum models. I also address the implications of this
framework on the possible time evolution of the fundamental constants of
Nature.
