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During the quasar era (redshifts between 1 and 3) Radio Galaxies (RGs) have been claimed to have substantially influenced the growth and evolution of large scale structures in the universe. In this dissertation I test the robustness of these exciting claims. In order to probe the impacts in more detail, good theoretical models for such RG systems are required. With this motivation, I seek to develop an essentially analytical model for the evolution of Fanaroff-Riley Class II radio galaxies both as they age individually and as their numbers vary with cosmological epoch. To do so, I first compare three sophisticated semi-analytical models for the dynamical and radio lobe power evolution of FR II galaxies, those given by Kaiser, Dennett-Thorpe & Alexander (1997, KDA), Blundell, Rawlings, & Willott (1999, BRW) and Manolakou & Kirk (2002, MK). I perform multi-dimensional Monte Carlo simulations leading to virtual radio surveys. The predictions of each model for redshift, radio power (at 151 MHz), linear size and spectral index are then compared with data. The observational samples are the low frequency radio surveys, 3CRR, 6CE and 7CRS, which are flux-limited and redshift complete. I next perform extensive statistical tests to compare the distributions of model radio source parameters and those of the observational samples. The statistics used are the 1-Dimensional and 2-Dimensional Kolmogorov-Smirnov (K-S) tests and the 4-variable Spearman partial rank correlation coefficient. I search for and describe the "best" parameters for each model. I then produced modifications to each of the three original models, and extensively compare the original and the modified model performances in fitting the data. The key result of my dissertation is that using the Radio Luminosity Function of Willott et al. (2001) as the redshift birth function of radio sources, the KDA and MK models perform better than the BRW models in fitting the 3CRR, 6CE and 7CRS survey data when using K-S based statistical tests, and the KDA model provides the best fits to the correlation coefficients. However, no pre-existing or modified model can provide adequate fits for the spectral indices. I also calculate the volume fraction of the relevant universe filled by the generations of radio galaxies over the quasar era. This volume filling factor is not as large as estimated earlier. Nonetheless, the allowed ranges of various model parameters produce a rather wide range of astrophysically interesting relevant volume fraction values. I conclude that the expanding RGs born during the quasar era may still play significant roles in the cosmological history of the universe.