  In this paper we present an overview on recent progress in studies of QCD at
finite temperature and densities within the functional renormalization group
(fRG) approach. The fRG is a nonperturbative continuum field approach, in which
quantum, thermal and density fluctuations are integrated in successively with
the evolution of the renormalization group (RG) scale. The fRG results for the
QCD phase structure and the location of the critical end point (CEP), the QCD
equation of state (EoS), the magnetic EoS, baryon number fluctuations
confronted with recent experimental measurements, various critical exponents,
spectral functions in the critical region, the dynamical critical exponent,
etc., are presented. Recent estimates of the location of the CEP from
first-principle QCD calculations within fRG and Dyson-Schwinger Equations,
which passes through lattice benchmark tests at small baryon chemical
potentials, converge in a rather small region at baryon chemical potentials of
about 600 MeV. A region of inhomogeneous instability indicated by a negative
wave function renormalization is found with $\mu_B\gtrsim 420$ MeV. It is found
that the non-monotonic dependence of the kurtosis of the net-proton number
distributions on the beam collision energy observed in experiments, could arise
from the increasingly sharp crossover in the regime of low collision energy.
