In this thesis, we study supersymmetry in various contexts. We begin with a study of perturbation theory of supersymmetric quantum electrodynamics. We note that computing the one-particle-irreducible effective action using a general $R_\xi$ gauge gives rise to infrared divergences, whose cancellation from physical quantities such as the electron pole mass occurs somewhat subtly. We discuss nonrenormalization theorems, both perturbative and non-perturbative.

Following that, we discuss models of inflationary cosmology, in which we employ supersymmetry as a tool for achieving nearly flat inflaton potentials. We systematically consider Planck-scale corrections to models of hybrid inflation, i.e. models in which inflation takes place on a pseudo-moduli space. We investigate the extent to which these models must be tuned to accommodate the 2013 Planck Satellite result for the spectral index, $n_s = 0.96$.

Finally, we consider the possibility that the lightest of the neutralinos, the superpartners of the neutral standard model Higgs and electroweak gauge bosons, may compose at least a fraction of the dark matter content of the universe. Working within the framework of the Minimal Supersymmetric Standard Model (MSSM), and allowing for the possibility that neutralinos make up only part of the observed dark matter relic density, we explore in detail which regions of parameter space are not excluded by null results from direct dark matter detection, assuming exclusive thermal production of neutralinos in the early universe, and illustrate the complementarity with current and future LHC searches for electroweak gauginos.