Supernovae observations and dark energy models In this thesis we review data sets available from various SNe groups like SNLS and HSST and utilize them to put constraints the cosmological parameters. We use the software CMBEASY to apply the MCMC method to models like lambdaCDM Constant Equation of State (EoS) w and Quintessence with our emphasis being on the IPL and Corasaniti model. We do the analysis using the Riess Gold Set the SNLS sample and the Union Data Set (with and without systematics). We have extended CMBEASY to include the Union Data Set and hence be up to date with latest observations. Our results show that omega m might be smaller than commonly assumed. Further we find that irrespective of model or data set chosen we get approximately the same value for omega m whereas this is not the case with w. The work in this thesis indicates that the emphasis in constructing new cosmological models should change from empirical to theoretical motivations.