<p>The properties of neutron stars and black holes are investigated within a class of alternative theories of gravity known as Scalar-Tensor theories, which extend General Relativity by introducing additional light scalar fields to mediate the gravitational interaction.</p> <p>It has been known since 1993 that neutron stars in certain Scalar-Tensor theories may undergo ‘scalarization’ phase transitions. The Weak Central Coupling (WCC) expansion is introduced for the purpose of describing scalarization in a perturbative manner, and the leading-order WCC coefficients are calculated analytically for constant-density stars. Such stars are found to scalarize, and the critical value of the quadratic scalar-matter coupling parameter β_s = −4.329 for the phase transition is found to be similar to that of more realistic neutron star models.</p> <p>The influence of cosmological and galactic effects on the structure of an otherwise isolated black hole in Scalar-Tensor gravity may be described by incorporating the Miracle Hair Growth Formula discovered by Jacobson in 1999, a perturbative black hole solution with scalar hair induced by time-dependent boundary conditions at spatial infinity. It is found that a double-black-hole binary (DBHB) subject to these boundary conditions is inadequately described by the Eardley Lagrangian and emits scalar dipole radiation.</p> <p>Combining this result with the absence of observable dipole radiation from quasar OJ287 (whose quasi-periodic ‘outbursts’ are consistent with the predictions of a general-relativistic DBHB model at the 6% level) yields the bound |φ/Mpl| < (16 days)^-1 on the cosmological time variation of canonically-normalized light (m < 10⁻²³ eV) scalar fields at redshift z ∼ 0.3.</p> / Doctor of Philosophy (PhD)