  We present recent results from lattice QCD relevant for the study of strongly
interacting matter as it is produced in heavy ion collision experiments. The
equation of state at non-vanishing density from a Taylor expansion up to
$6^{th}$ order will be discussed for a strangeness neutral system and using the
expansion coefficients of the series limits on the critical point are
estimated. Chemical freeze-out temperatures from the STAR and ALICE
Collaborations will be compared to lines of constant physics calculated from
the Taylor expansion of QCD bulk thermodynamic quantities. We show that
qualitative features of the $\sqrt{s_{NN}}$ dependence of skewness and kurtosis
ratios of net proton-number fluctuations measured by the STAR Collaboration can
be understood from QCD results for cumulants of conserved baryon-number
fluctuations. As an example for recent progress towards the determination of
spectral and transport properties of the QGP from lattice QCD, we will present
constraints on the thermal photon rate determined from a spectral
reconstruction of continuum extrapolated lattice correlation functions in
combination with input from most recent perturbative calculations.
