Ultra-relativisitic heavy ion collisions produce quark gluon plasma-a hot and dense soup of deconfined quarks and gluons akin to the early universe. We study two models in the context of these collisions namely, Polyakov Quark Meson Model (PQM) and Hadron Resonance Gas Model (HRGM).The PQM Model provides us with a simple and intuitive understanding of the QCD equation of state and thermodynamics at non zero temperature and baryon density while the HRGM is the principle model to analyse the hadron yields measured in these experiments across the entire range of beam energies. We study the effect of including the commonly neglected fermionic vacuum fluctuations to the (2+1) flavor PQM model. The conventional PQM model suffers from a rapid phase transition contrary to what is found through lattice simulations. Addition of the vacuum term tames the rapid transition and significantly improves the model’s agreement to lattice data. We further investigate the role of the vacuum term on the phase diagram. The smoothening effect of the vacuum term persists even at non zero . Depending on the value of the mass of the sigma meson, including the vacuum term results in either pushing the critical end point into higher values of the chemical potential or excluding the possibility of a critical end point altogether. We compute the fluctuations(correlations) of conserved charges up to sixth(fourth) order. Comparison is made with lattice data wherever available and overall good qualitative agreement is found, more so for the case of the normalised susceptibilities. The model predictions for the ratio of susceptibilities approach to that of an ideal gas of hadrons as in HRGM at low temperatures while at high temperature the values are close to that of an ideal gas of massless quarks. We examine the stability of HRGMs by extending them to take care of undiscovered resonances through the Hagedorn formula. We find that the influence of unknown resonances on thermodynamics is large but bounded. We model the decays of resonances and investigate the ratios of particle yields in heavy-ion collisions. We find that extending these models do not have much effect on hydrodynamics but the hadron yield ratios show better agreement with experiment. In principle HRGMs are internally consistent up to a temperature higher than the cross over temperature in QCD; but by examining quark number susceptibilities we find that their region of applicability seems to end even below the QCD cross over.