While general relativity is a very successful theory of gravity, having thus far passed all observational tests with flying colors, it is thought to be incomplete. Indeed, we lack an ultimate high energy theory in which general relativity and quantum mechanics are both valid. We consider extensions to the action of general relativity, and seek to place constraints on these alternative theories using astrophysical tests. General relativity has been extensively tested in the solar system, but not with precision in strong gravity systems. We discuss constraints that could be placed on alternative theories using neutron stars. We find that we may not be able to distinguish between general relativity and some alternative theories in the spacetimes around black holes. We also discuss constraints from cosmological tests, and show that instabilities can appear.Adding higher-order terms to the action of general relativity can introduce new dynamical degrees of freedom and instabilities. From the standpoint of effective field theory however, these alternative theories are inconsistent because they are not unitary. In an effective field theory, no new degree of freedom is introduced. This also means that extra polarizations of gravitational waves, which are predicted by some alternative theories, would not be present in an effective field theory.We then consider an effective field theoretic formulation for gravitational radiation called Non-Relativistic General Relativity (NRGR). We study the gravitational wave emission in non-relativistic coalescing compact binaries, which are thought to be powerful emitters of gravitational waves. While NRGR is based on the post-newtonian (PN) approximation to general relativity, and should therefore be in complete agreement with other post-newtonian methods, the effective field theory approach provides two major advantages: it provides a consistent framework for the dynamics using a lagrangian formulation; also, one can in principle compute observables to all orders in the orbital velocity in a systematic way. We provide a brief overview of NRGR methods, and present the NRGR calculation of the subleading spin-orbit correction to the newtonian potential.

In this thesis I test the modified Newtonian dynamics as an alternative to the cold dark matter hypothesis. In the Milky Way, I show that the dynamics of the dwarf galaxies are well described by the paradigm and I confirm its distant low surface brightness globular clusters provide a strong test, for which I make predictions. Through analysis of a sample of 26 X-ray bright galaxy groups and clusters I demonstrate that the three active neutrinos and their anti-particles are insufficient to reconcile modified Newtonian dynamics with the observed temperatures of the X-ray emitting gas, nor with weak-lensing measurements, in particular for the bullet cluster. To this end, I propose an 11eV sterile neutrino to serendipitously resolve the residual mass problem in X-ray bright groups and clusters, as well as matching the angular power spectrum of the Cosmic Microwave Background. With this in mind, I show that the large collision velocity of the bullet cluster and the high number of colliding clusters is more naturally reproduced in MOND than in standard dynamics.