Determination of the spatial distribution and quantification of concentration of pure beta- and photon-emitting radionuclides in absorbing media by external measurements is the subject of this study. Measurements of radiation and the operation of radiation detectors are based on the radiation interactions with matter and the theory governing these interactions has been discussed. Various techniques for localising pure beta- and photon-emitting radionuclides situated inside attenuating media have been suggested on a theoretical basis, and have been experimentally shown to work successfully. Most of the work is on single photon emission computed tomography (SPECT). The theory of mathematical reconstruction of a two dimensional distribution from its projections is discussed and reconstruction techniques and their relative merits and demerits have been reviewed. SPECT seeks the determination of absolute regional radionuclide concentrations as a function of time. A SPECT system has been developed by modifying an existing transmission CT scanner and the reconstruction algorithms. The performance of the SPECT system has been tested for a number of point sources and various extended sources in gas, liquid and solid forms. The SPECT scanner in its present design is capable of performing in both the transmission and emission modes. The characteristics of the SPECT scanner, including the detector efficiency, spatial resolution and the effect of collimator size, have been studied experimentally. The major problems faced by SPECT include the solid angle effect, which influences the collection efficiency, in scattered radiation, and attenuation of photons inside the surrounding medium. These problems together with their various possible solutions have been discussed in detail. Methods for compensation for solid angle variation, in scattered radiation and photon attenuation have been devised and used successfully to compensate the projection data.