We present a study of discrete radio sources in the Magellanic Clouds (MCs) using the latest large-scale radio surveys made with the Parkes radio telescope between 1.4 and 8.55GHz. These surveys achieved higher sensitivity than previous surveys done with the Parkes telescope and so the number of discrete radio sources detected towards the MCs has increased by factor of five. Also, we have obtained improved positions, flux densities and radio spectral indices for all of these sources. A total of 483 sources towards the Large Magellanic Cloud (LMC) and 224 towards the Small Magellanic Cloud (SMC) have been detected at at least one radio frequency. Most of the MC's sources have been classified in one of three groups: SNRs, HII regions or background sources according to classification criteria established here. In total, 209 discrete radio sources in the LMC and the 37 sources in the SMC are classified here to be either HII regions or SNRs. We investigate their luminosity functions as well as the statistics of background sources behind the MCs. Also, we examine the distribution of SNRs and HII regions in the MCs.