  We present our most recent investigations on the QCD cross-over transition
temperatures with 2+1 staggered flavours and one-link stout improvement [JHEP
1009:073, 2010]. We extend our previous two studies [Phys. Lett. B643 (2006)
46, JHEP 0906:088 (2009)] by choosing even finer lattices ($N_t$=16) and we
work again with physical quark masses. All these results are confronted with
the predictions of the Hadron Resonance Gas model and Chiral Perturbation
Theory for temperatures below the transition region. Our results can be
reproduced by using the physical spectrum in these analytic calculations. A
comparison with the results of the hotQCD collaboration is also discussed.
