Dark energy is the simplest and the most standart explanation to account for the observed accelerated expansion of the universe. In this thesis we use the term 'dark energy' in its standart meaning i.e. a field or fluid that is responsible for the cosmic acceleration in the frame work of general relativity. Meanwhile extra dimensions is an attractive framework to understand many otherwise unexplained physical phenomena in a clear, simple formulation. Therefore the study of extra dimensional cosmological models is an attractive area of study. In this thesis we have considered viability of extra dimensional cosmological models in the light of the accelerated expansion of the universe. We have confirmed the results of studies that have shown the incompatibility of a broad class of extra dimensional cosmological models with a dark energy of an equation of state close to that of cosmological constant. We have discussed also possible theoritical and vational ways to avoid the no-go theorems for extra dimensional cosmological models as well.