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In this talk I will explore several theoretical issues in applying the S-matrix formulation of statistical mechanics to describe the density of states of interacting hadrons. This allows a consistent treatment of many dynamical structures such as overlapping resonances, poles and roots. I will discuss how inconsistencies between theory and experiment, e.g. the proton puzzle and the proton to Lambda ratio, may be resolved by considering some essential features of the empirical baryon spectrum. These dynamical features are also crucial for understanding the Lattice results on thermal QCD, such as the baryon electric charge correlation.
(If time permits, recent progress on confinement models of quarks and gluons will be reported.)