In this thesis I have presented the findings of my research pursued during my Ph.D. study. The purpose of this thesis was to study different theoretical ideas in high energy physics model building addressed primarily towards understanding the fermion mass problem and the gauge hierarchy problem. These include: Anomalous flavor U/(1) symmetry and its experimental implications, finite GUT models with discrete family symmetry, and a product GUT model in a 2D deconstructed theory space. The second and third chapters of the thesis describe our study of lepton flavor violation (LFV) and electric dipole moments (EDM) induced by a flavor-dependent anomalous U/(1) gauge symmetry of string origin. The models considered also address the fermion mass hierarchy problem successfully. We have shown that the U/(1) sector induces significant LFV and EDMs through the SUSY breaking parameters. These effects arise via renormalization group evolution of the parameters in the momentum regime between the string and the anomalous U/gauge symmetry of string origin. The models considered also address the fermion mass hierarchy problem successfully. We have shown that the U(1) sector induces significant LFV and EDMs through the SUSY breaking parameters. These effects arise via renormalization group evolution of the parameters in the momentum regime between the string and the anomalous U(1) breaking scale. The fourth chapter of the thesis contains our work on a concrete realization of SUSY breaking using interference between the anomalous U(1) flavor gauge symmetry and a strongly coupled SU(Nc), leading to the so called Split SUSY spectrum where the sfermions and the gravitino acquire masses of order 10(^5)/10(^8) GeV while the gauginos and the Higgsinos have masses of order 10(^2)/10(^3) GeV. We have cal- culated the leading order supergravity corrections and have presented a class of explicit models of Split SUSY which are phenomenologically consistent. In the fifth chapter I have presented models for realistic quark masses and mixings in the context of finite SU(5) GUT where in the B functions for the gauge and the Yukawa couplings vanish to all orders in perturbation theory. The models pre-sented are based on non-Abelian discrete symmetries. In the case of (Z4)3xP and A4 symmetries we have found models finite to all order of perturbation theory while in the case of an S4 symmetry we have found a model which is two-loop finite. In the sixth chapter I have presented a model wherein the observed fermion masses and mixing angles emerge from a deconstructed U(1) theory space with a disk structure in SU(5)'xSU(5)'' product GUT. Below the B - L breaking scale, the effective Yukawa couplings and mixing matrices of the fermions are correctly reproduced through non-renormalizable operators. In our model, both the fermion mass matrix structures, and supersymmetry breaking (as a global twist of RP2) can be addressed in the same theory space consistent with phenomenology and anomaly cancelation
