This dissertation presents a number of projects relating to searching for new physics with the ATLAS experiment at the Large Hadron Collider (LHC), with the main focus being a search for hypothetical massive, charged, long-lived particles. This search was conducted using 140.1 fb^−1 of proton-proton collision data with a center of mass energy √s = 13 TeV at the LHC. These particles are expected to move at speeds slower than known Standard Model (SM) particles, and are identified via their large transverse momentum and large specific ionization energy losses dE/dx. No significant deviation from the Standard Model was observed, and exclusion limits were placed on the mass and lifetime of the supersymmetric partner to the tau lepton. This dissertation also documents research into the methods of reconstructing particle tracks at ATLAS in preparation for the inner detector upgrade and the evolution of the LHC to the High-Luminosity LHC (HL-LHC). The HL-LHC will see an increased collision rate and a more hazardous radiation environment which necessitates the development of new detector hardware and new track reconstruction algorithms. In addition, this dissertation briefly discusses the prospects of the next generation of particle collider experiments.