The scattering of radio waves and multipath propagation in the interstellar medium (ISM) of our Galaxy produces various observable phenomena such as the interstellar scintillation (ISS) and angular broadening of compact radio sources, as well as the temporal smearing of impulsive radio bursts. These effects have been harnessed as probes of the ISM and of the background sources themselves. On the other hand, scattering in the intergalactic medium (IGM) has yet to be incontrovertibly detected, and is a main target of future surveys and instruments, since the IGM constitutes the main reservoir of baryons in the Universe. The first part of this thesis makes use of observational data from a survey of interstellar scintillation (ISS) of compact Active Galactic Nuclei (AGNs) to further investigate the nature of these sources, the ISM, ISS, and methods of handling variability data in the presence of stochastic and systematic errors. This study therefore acts as a technical and scientific demonstrator for future large-scale surveys of ISS and the variable radio sky.The results of this study further strengthen the link between AGN variability at radio wavelengths with ISS, and show how the spectral indices and mean flux densities of the sources, as well as observing frequencies, all influence the observed ISS characteristics. Six new rapid scintillators with characteristic time-scales of . 2 hours were identified in the sample, providing new insight into the origin of rapid and extreme scintillation. This thesis also presents the first detailed investigation into the origin of the suppresion of ISS for AGNs at z & 2 as discovered by the Micro-Arcsecond Scintillation Induced Variability (MASIV) Survey, a precursor to the present work. I determined that the redshift dependence of ISS is partially linked to the steepening of source spectral indices (_8.4 4.9) with redshift, caused either by selection biases or AGN evolution, coupled with weaker ISS in the _8.4 4.9 < −0.4 sources. Selecting only the −0.4 < _8.4 4.9 < 0.4 sources, the redshift dependence of ISS is still significant, but is not significantly steeper than the expected (1 + z)0.5 scaling of source angular sizes due to cosmological expansion for a brightness temperature and flux-limited sample of sources. No significant evidence of scatter broadening in the IGM was found, placing the strongest upper limit to date of . 8μas at 4.9 GHz for sight-lines to the most compact, _ 10μas sources.The second part of the thesis makes use of this observational limit on IGM scattering, together with extensions of ISM scattering models to cosmological scales, to investigate the detectability of the IGM with next generation radio arrays. While angular broadening in the IGM is insignificant for most sight-lines and appears difficult to resolve even with space VLBI, significant temporal smearing of extragalactic radio transients cannot be ruled out, and provides the best chance of detecting IGM scattering. However, the corresponding reduction in the signal-to-noise ratio of these bursts potentially places crippling limits on the detectability of such transient pulses in the first place, particularly at frequencies below _ 1 GHz. This has important ramifications for the optimization of observational strategies for detecting extragalactic radio transients with low-frequency instruments such as the Murchison Widefield Array (MWA), the Low Frequency Array (LOFAR) and the low frequency component of the Square Kilometre Array (SKA)
