The purpose of this thesis is to compare the quintessence models. The ideas of quintessence and particle physics realization of quintessence models are reviewed. The field solutions of typical quintessence with exponential and negative power law potentials are derived in detail. From the field solutions it can beseen that the quintessence with these potentials cannot satisfy the observational constraints. The ways for modifying these quintessence models are reviewed. Although some quintessence models which arise from supersymmetry and supergravity theories can satisfy the observational conditions but these quintessence models have some problems when supersymmetry is broken.
