To study the origin of radio emission and the cosmic evolution of radio detected radiatively efficient active galactic nuclei, I used the radio data of sources detected within the COSMOS and XXL-S sky fields, which were previously cross-correlated with available multiwavelength data. A sample of 1,604 moderate-to-high radiative luminosity AGN (HLAGN) detected within the COSMOS field was selected using criteria sensitive to the X-ray, MIR and optical emissions expected to arise from the efficient accretion onto a supermassive black hole. I developed a statistical method of radio luminosity decomposition, which I used to separate the observed HLAGN radio emission into AGN and star formation-related contributions to the radio luminosity. This was done via the so-called AGN fraction, defined as the fractional contribution of the AGN-related radio emission to the total observed radio emission. I found that the majority of HLAGN (~ 68%) is dominated by star formation-related radio emission (0_AGN < 0.5). However, there are ~ 32% of HLAGN whose radio emission is dominated by the AGN-related radio emission (0.5 ≤ f_AGN ≤ 1). The AGN fractions obtained for each source via the decomposition method were used to scale the total radio luminosity down to the radio AGN luminosity. Using the obtained AGN luminosities, the radio AGN luminosity functions were constructed and constrained out to z ~ 6. The number and luminosity densities of HLAGN were further constrained, with the peak of the evolution found in the cosmic epoch when the universe was 4 billion years old (z ~ 1 - 2.5). Next, by combining the COSMOS HLAGN data-set with the radio-to-X-ray data for a sample of high-excitation radio galaxies within the XXL-S field, I studied a sample of 274 radio and X-ray selected quasars (XQSOs) at 0.25 < z < 6.1. These were selected by a criterion of L_X[2 - 10 keV] ≥ 10^44 ergs^-1 which broadly selects quasars. By calculating the radio loudness of these sources using four different definitions and applying criteria as commonly used in the literature to separate them into radio-quiet and radio-loud AGN, I found that 18 - 73% of XQSOs are selected as radio-loud. This significant disagreement arises both from the different flux density thresholds of the COSMOS and XXL-S radio surveys, as well as because of different criteria that capture different processes related both to star formation and AGN activity. To study further the origin of radio emission in XQSOs, I constructed radio luminosity functions of XQSOs and constrained their shape in six redshift bins at 0.5 < z < 3.75. The lower-1.4 GHz luminosity end shows a higher normalization than expected only from AGN contribution in all studied redshift bins. I found that the so-called ‘bump’ is mostly dominated by emission due to star-forming processes within the host galaxies of XQSOs. As expected, AGN-related radio emission is the dominant contribution at the higher-luminosity end of the RLF. To test if the environment plays a significant role in the presence of AGN-dominated radio emission in some radiatively efficient AGN, I cross-correlated the HLAGN sample with the X-ray group catalog available within COSMOS finding that 43 HLAGN at 0.2 < z < 1.3 are located within the X-ray groups. For these sources, I found a trend of decreasing AGN fractions with increasing distance from the X-ray group center.