Comprehensive and robust analysis of galaxies found throughout cosmic time provides the means to probe the underlying characteristics of our Universe. Coupling observations and theory, spectral energy distribution (SED) fitting provides a method to derive the intrinsic properties of distant galaxies which then aid in defining galaxy populations and constraining current galaxy formation and evolution scenarios. One such population are the sub-millimeter galaxies (SMGs) whose high infrared luminosities -- typically associated with dust-obscured star formation -- and redshift distribution places them as likely key components in galaxy evolution. To fully analyze these systems, however, requires a near complete sampling of the full SED, detailed models that encapsulate the variety of physical processes and sophisticated methods for comparing the data and models. In this dissertation, we present the general propose, Monte Carlo Markov Chain (MCMC) based SED fitting routine SED Analysis Through Markov Chains (SATMC) and the insight we have gained in modeling a sample of AzTEC 1.1mm-detected SMGs. The MCMC engine and Bayesian formalism used in the construction of SATMC offers a unique view at the constraints on model parameter space that are often grossly simplified in traditional SED fitting methods. We first present the motivation behind SATMC and its MCMC algorithm. We also highlight a series of test cases that verify not only its reliability but its versatility to various astrophysical applications, including the field of photometric redshift estimation. We then present the AzTEC SMG sample and preliminary results obtained through counterpart identification, X-ray spectral modeling and SED fitting with SATMC. Finally, we present the latest work in detailed SED analysis of SMGs and how these results influence our understanding of the SMG population.