  Galileon gravity offers a robust gravitational theory for explaining cosmic
acceleration, having a rich phenomenology of testable behaviors. We explore
three classes of Galileon models -- standard uncoupled, and linearly or
derivatively coupled to matter -- investigating the expansion history with
particular attention to early time and late time attractors, as well as the
linear perturbations. From the relativistic and nonrelativistic Poisson
equations we calculate the generalizations of the gravitational strength
(Newton's constant), deriving its early and late time behavior. By scanning
through the parameters we derive distributions of the gravitational strength at
various epochs and trace the paths of gravity in its evolution. Using
ghost-free and stability criteria we restrict the allowed parameter space,
finding in particular that the linear and derivative coupled models are
severely constrained by classical instabilities in the early universe.
