Understanding the electronic structure and dynamics of cyclic organic molecules is becoming increasingly the subject of investigations from different perspectives due to their unique chemical and physical properties. Since they are largely involved in the biochemistry of living organisms, studies on this class of compounds are also valuable to understand biologically relevant complex systems. Compared to other techniques, high-order harmonic generation (HHG) has been increasingly considered as a powerful spectroscopic tool with Angstrom spatial and attosecond temporal resolutions. This thesis demonstrates that high-order harmonic spectroscopy is capable of providing structural and dynamical information on the electronic systems of representative cyclic organic molecules comprising randomly oriented five-membered or six-membered rings. The first part of this thesis shows that the HHG from these molecules is sensitive to their aromatic character, which results from the de-localized pi electrons, and can potentially be a useful qualitative measure of aromaticity. We show that the advantage of utilizing HHG in this direction stems from the result that only pi molecular orbitals, associated with aromatcity, are responsible for the HHG emission in aromatic systems. The capability of HHG to distinguish cyclic isomers is demonstrated in the case of xylene molecules. Supported by numerical calculations, differences in the isomers are attributed to both tunnel ionization and photorecombination, the first and last steps of HHG. These results enable further HHG-based time-resolved studies of the dynamics associated with isomeric effects that these molecules exhibit. The present work also challenges the well-established prediction that strong field ionization from a molecular orbital is suppressed along nodal planes, where the electron density is zero. In fact, our study shows that considerable tunnel ionization in some cyclic molecules can occur near or along nodal planes. This unusual ionization is reported to have its signature on the quantitative and qualitative dependence of harmonic yield on laser ellipticity. The high symmetry displayed by the cyclic molecule, 1,4 cyclohexadiene, is shown to leave its imprints on the HHG in the form of structural interferences even if the target is randomly oriented. Two-color HHG from this molecule also indicates that hole dynamics could be involved in the generation process. A general study on high harmonic spectroscopy of the Cooper minimum in molecules is also reported. The presence of this minimum could affect the interpretation of harmonics spectra in any molecule containing S or Cl atoms. The molecular environment is shown to influence the position of this spectral modulation.