  We present results from lattice QCD calculations for $2^{nd}$ and $4^{th}$
order cumulants of conserved charge fluctuations and correlations, and compare
these with various HRG model calculations. We show that differences between HRG
and QCD calculations already show up in the second order cumulants close to the
pseudo-critical temperature for the chiral transition in (2+1)-flavor QCD and
quickly grow large at higher temperatures. We also show that QCD results for
strangeness fluctuations are enhanced over HRG model calculations which are
based only on particles listed in the Particle Data Group tables as 3-star
resonances. This suggests the importance of contributions from additional
strange hadron resonances. We furthermore argue that additional (repulsive)
interactions, introduced either through excluded volume (mean field) HRG models
or the S-matrix approach, do not improve the quantitative agreement with
$2^{nd}$ and $4^{th}$ order cumulants calculated in lattice QCD. HRG based
approaches fail to describe the thermodynamics of strongly interacting matter
at or shortly above the pseudo-critical temperature of QCD.
