  After briefly reviewing recent progress by the HotQCD collaboration in
studying the 2+1 flavor QCD equation of state, we will focus on results on
fluctuations of conserved charges by the BNL-Bielefeld and HotQCD
collaborations. Higher order cumulants of the net-charge distributions are
increasingly dominated by a universal scaling behavior, which arises due to a
critical point of QCD in the chiral limit. Considering cumulants up to the
6^{th} order, we observe that they generically behave as expected from
universal scaling laws, which is quite different from cumulants calculated
within the hadron resonance gas model. Taking ratios of these cumulants, we
obtain volume independent results that can be compared to the experimental
measurements. We will argue that the freeze-out chemical potentials and the
freeze-out temperature, usually obtained by a HRG model fit to the measured
hadronic yields, can also be obtained in a model independent way from ab-initio
lattice QCD calculations by utilizing observables related to conserved charge
fluctuations. Further, we will show that the freeze-out strangeness and
electric charge chemical potentials can be fixed by imposing strangeness
neutrality and isospin asymmetry constraints in the lattice QCD calculations,
in order to accommodate conditions met in heavy ion collisions. All results
have been obtained with the highly improved staggered quark action (HISQ) and
almost physical quark masses on lattices with temporal extent of
N_\tau=6,8,10,12.
