The Standard Model of particle physics has been tested over many years with many ex- periments and has predicted experimental results with remarkable accuracy. In 2012, the last piece of the Standard Model, the Higgs boson, was discovered by the experiments ATLAS and CMS at the Large Hadron Collider (LHC). Although this completes the Standard Model, this by no means completes our picture of the physics that describes the observable universe. Several phenomena and measurements remain unexplained by the Standard Model including gravity, dark matter, the baryon-antibaryon asymmetry of the universe and more. One of the primary goals of the LHC and the ATLAS experiment are to search for extensions and modifications to the Standard Model that could help to explain these phenomena. This the- sis presents three areas where I made major contributions. The first is in the identification of prompt electrons in ATLAS using a likelihood method both in the online trigger system and in offline data analysis. Prompt electrons are ubiquitous in the signatures of electroweak physics, one of the cornerstones of the ATLAS physics program. Next I present a search for new physics in low-mass (65-110 GeV) diphoton events. This is a model independent search that is motivated by several extensions to the Standard Model including the two Higgs doublet model where new scalars can appear as lighter versions of the Standard Model Higgs. No evidence for a new narrow resonance is found, so limits ranging from 30 to 101 fb are set on the production cross section of such a resonance, assuming that its branching fraction to two photons is 100 percent. The sensitivity of these results are limited by the systematic uncertainties due to the potential spurious signals introduced by the two-photon non-resonant Standard Model background. My third contribution was an initial investigation of a new method to model this background using Gaussian Process Regression.