The study of radicals is a fascinating undertaking that, through a combination of structural studies, electron paramagnetic resonance spectroscopy, and quantum chemical calculations, provides informative insights into the electronic structures in odd-electron systems. In the present dissertation, quantum chemical methods have been used to aid in the interpretation of experimental observations gathered for a number of main group radicals. A theoretical analysis of the electronic structures of some inorganic diradicaloids is also presented. A detailed understanding of the molecular and electronic structures of these systems, and the factors which govern them, is essential for future studies of their incorporation into useful materials. The research presented in the first half of this thesis describes the synthesis and characterization of new stable radicals of the main group elements. It resulted in the preparation of multiple stable and persistent systems incorporating the tetraimidophosphate dianion radical {Li2[P(NtBu)3(NSiMe3)]}•, as well as in the synthesis of the first stable metal complexes of the boraamidinato radical {[PhB(NtBu)2]−}•. The spectroscopic and density functional studies described herein played a crucial role in the characterization of these novel paramagnetic species. The results from theoretical calculations on some stable paramagnetic complexes of the 1,4-diaza-1,3-butadiene ligand with gallium are also presented. The computational data provided valuable information aiding the interpretation of their EPR spectra as well as the analysis of the solution behaviour of some related radical species. The second half of this thesis summarizes the key findings from theoretical investigations of the electronic structures of some main group singlet diradicaloids. The results reveal that, despite opposed claims, stable main group singlet diradicaloids with significant amounts of diradical character still await their discovery. The quantum chemical calculations also demonstrate the importance of correct theoretical description of static electron correlation effects in these systems, and provide high-level computational data which can be used in the experimental efforts focused on the preparation of the conducting polymers (SeN)x and (SeNSN)x.