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In this thesis, we explore two approaches to string phenomenology. In thefirst half of the work, we investigate M-theory compactifications on spaceswith co-dimension four, orbifold singularities. We construct M-theory onC^2/Z_N by coupling 11-dimensional supergravity to a seven-dimensionalYang-Mills theory located on the orbifold fixed-plane. The resulting action issupersymmetric to leading non-trivial order in the 11-dim Newton constant. Wethereby reduce M-theory on a G2 orbifold with C^2/Z_N singularities, explicitlyincorporating the additional gauge fields at the singularities. We derive theKahler potential, gauge-kinetic function and superpotential for the resultingN=1 four-dimensional theory. Blowing-up of the orbifold is described by a Higgseffect and the results are consistent with the corresponding ones obtained forsmooth G2 spaces. Further, we consider flux and Wilson lines on singular lociof the G2 space, and discuss the relation to N=4 SYM theory.  In the second half, we develop an algorithmic framework for E8 x E8 heteroticcompactifications with monad bundles. We begin by considering cyclic Calabi-Yaumanifolds where we classify positive monad bundles, prove stability, andcompute the complete particle spectrum for all bundles. Next, we generalize theconstruction to bundles on complete intersection Calabi-Yau manifolds. We showthat the class of positive monad bundles, subject to the heterotic anomalycondition, is finite (~7000 models). We compute the particle spectrum for thesemodels and develop new techniques for computing the cohomology of line bundles.There are no anti-generations of particles and the spectrum is manifestlymoduli-dependent. We further study the slope-stability of positive monadbundles and develop a new method for proving stability of SU(n) vector bundles.

Heterotic and M-theory Compactifications for String Phenomenology