The search for fluctuations in the Cosmic Microwave Background (CMB) is one of the most important topics in modern cosmology, since their detection would reveal a great many details about the early universe and, in particular, the nature of the primordial density perturbations giving rise to the galaxies and clusters of galaxies seen in the universe today. However, the search for such anisotropies is not trivial- none have been detected as yet - largely as a consequence of the fact that all radiative astrophysical sources can give rise to anisotropic foregrounds which confuse the search for genuine cosmological signals. In this thesis, a detailed study is made of the contribution of such foregrounds to searches for CMB fluctuations. After Chapter 1 summarises the theoretical and observational status of the subject, Chapters 2, 3 and 4 consider the foreground resulting from the Galaxy. It is found that frequencies in excess of 20 GHz are required to reduce the Galactic Synchrotron Radiation to a level where genuine anisotropies might be detected (the synchrotron emission is almost certainly responsible for a previously claimed detection), and that dust emission, especially if very cold dust exists which is unseen and possibly untraced by the dust responsible for the emission seen in the IRAS 100µm passband, can seriously constrain high frequency searches. In Chapter 4 a model is derived for the overall Galactic foreground including a separation of the thermal and non-thermal radio emission in the Galactic plane. Comparison with observations at 10 and 15 GHz suggests that the model is ~ 10%- 20% accurate on average at these frequencies, and maps of the predicted emission at the COBE frequencies 31.5, 53, and 90 GHz are provided. .4. search is made for a frequency window and sky region which minimises the Galactic contribution to the fluctuation measurements: highly sensitive, high resolution searches should be designed with these values in mind. Chapter 5 investigates the anisotropies resulting from discrete extragalactic sources, in particular, the far-infrared emission from dust in spiral galaxies and the integrated radio emission due to radio galaxies, QSOs etc. A frequency window of ~ 30 - 100 GHz is found to minimise both Galactic and extragalactic foreground anisotropies. Chapter 6 considers several cosmological models which could generate the recently observed large-scale structure in the galaxy- distribution: these are constrained by CMB anisotropy limits. It is concluded that genuine cosmological variations in the CMB temperature are now close to detection if the observed galaxy- structures are real. Chapter 7 indicates some future projects which should help in the detection and interpretation of CMB fluctuations.