The standard models of particle physics and cosmology have been tremendously successful at describing our universe. At the same time, there are a number of glaring discrepancies that suggest new physics just around the high energy corner. Supersymmetry has been shown to help stabilize the Higgs mass while offering a number of prospects for cosmological solutions. One of these prospects is a super weakly interacting massive particle (SuperWIMP), the supersymmetric partner of the graviton, the gravitino. SuperWIMPs have been shown to be consistent with all cosmological observations from the dark matter relic density to big bang nucleosynthesis abundances and the inferred galactic power spectrum. This thesis is the accumulation of work studying the collider phenomenology of long-lived sleptons that decay to gravitinos. An extended minimal supergravity model with a large parameter space containing long-lived sleptons is shown to be consistent with particle physics constraints. The discovery potential of this model at the Large Hadron Collider (LHC) is analyzed, and it is shown that long-lived sleptons can be discovered during the first year, assuming 4 fb-1 physics run of the LHC. The spin is then shown to be measurable during the second year's physics run of 30 fb-1 . Finally, a trap is proposed so that the lifetime of these sleptons can be measured, illuminating the prospects of the first high energy measurement of the Planck scale.
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