  In this thesis we examine three different models in the MSSM context, all of
which have significant supergravity anomaly contributions to their soft masses.
These models are the so-called Minimal, Hypercharged, and Gaugino Anomaly
Mediated Supersymmetry Breaking models. We explore some of the string
theoretical motivations for these models and proceed by understanding how they
would appear at the Large Hadron Collider (LHC). Our major results include
calculating the LHC reach for each model's parameter space and prescribing a
method for distinguishing the models after the collection of 100 fb^-1 at
sqrt{s}=14 TeV. AMSB models are notorious for predicting too low a dark matter
relic density. To counter this argument we explore several proposed mechanisms
for $non$-$thermal$ dark matter production that act to augment abundances from
the usual thermal calculations. Interestingly, we find that future direct
detection dark matter experiments potentially have a much better reach than the
LHC for these models.
