Assuming the redshifts of quasars are cosmological, their distribution in space is investigated by means of new test, the luminosity- volume test (Chapter I), which is shown to be far more powerful than the magnitude-redshift test. In most relativistic cosmological models, strong * evolutionary factors must be influencing the distribution of quasars in space, and possible explanations are discussed qualitatively and quantitatively. The similar behaviour of the stronger radio-galaxies strengthens the link between the two classes of source. Less direct information about more remote parts of space is obtained by the interpretation of the radio source-counts (Chapter III) and the integrated radio and X-ray background intensities (Chapter IV). Assumptions have to be made about the physical properties of sources, particularly the magnetic field, and a number of different models for the structure of radio-sources are discussed in Chapter II. Evidence is presented against the idea that the radio-emitting components are ejected from the parent galaxies at relativistic speeds. Models are considered in which relativistic electrons are generated continuously in the radiating components.