List of Figures

	Figure 1: Selected tests of the weak equivalence principle, showing bounds on $η$ , which measures fractional difference in acceleration of different materials or bodies. The free-fall and Eöt-Wash experiments were originally performed to search for a fifth force (green region, representing many experiments). The blue band shows evolving bounds on $η$ for gravitating bodies from lunar laser ranging (LLR).
	Figure 2: Selected tests of local Lorentz invariance showing the bounds on the parameter $δ$ , which measures the degree of violation of Lorentz invariance in electromagnetism. The Michelson–Morley, Joos, Brillet–Hall and cavity experiments test the isotropy of the round-trip speed of light. The centrifuge, two-photon absorption (TPA) and JPL experiments test the isotropy of light speed using one-way propagation. The most precise experiments test isotropy of atomic energy levels. The limits assume a speed of Earth of $− 1 370 km s$ relative to the mean rest frame of the universe.
	Figure 3: Selected tests of local position invariance via gravitational redshift experiments, showing bounds on $α$ , which measures degree of deviation of redshift from the formula $Δ ν∕ν = ΔU ∕c2$ . In null redshift experiments, the bound is on the difference in $α$ between different kinds of clocks.
	Figure 4: Geometry of light deflection measurements.
	Figure 5: Measurements of the coefficient $(1 + γ )∕2$ from light deflection and time delay measurements. Its GR value is unity. The arrows at the top denote anomalously large values from early eclipse expeditions. The Shapiro time-delay measurements using the Cassini spacecraft yielded an agreement with GR to $10− 3$ percent, and VLBI light deflection measurements have reached 0.01 percent. Hipparcos denotes the optical astrometry satellite, which reached 0.1 percent.
	Figure 6: Constraints on masses of the pulsar and its companion from data on B1913+16, assuming GR to be valid. The width of each strip in the plane reflects observational accuracy, shown as a percentage. An inset shows the three constraints on the full mass plane; the intersection region (a) has been magnified 400 times for the full figure.
	Figure 7: Plot of the cumulative shift of the periastron time from 1975 – 2005. The points are data, the curve is the GR prediction. The gap during the middle 1990s was caused by a closure of Arecibo for upgrading. Image reproduced with permission from [409], copyright by AAS.
	Figure 8: Constraints on masses of the pulsar and its companion from data on J0737–3039A,B, assuming GR to be valid. The inset shows the intersection region magnified by a factor of 80. Image courtesy of M. Kramer.
	Figure 9: Bounds on the scalar–tensor parameters $α 0$ and $β 0$ from solar-system and binary pulsar measurements. Bounds from tests of the Nordtvedt effect using lunar laser ranging and circular pulsar–white-dwarf binary systems are denoted LLR and SEP, respectively. Image reproduced with permission from [164], copyright by the authors.
	Figure 10: The six polarization modes for gravitational waves permitted in any metric theory of gravity. Shown is the displacement that each mode induces on a ring of test particles. The wave propagates in the $+z$ direction. There is no displacement out of the plane of the picture. In (a), (b), and (c), the wave propagates out of the plane; in (d), (e), and (f), the wave propagates in the plane. In GR, only (a) and (b) are present; in massless scalar–tensor gravity, (c) may also be present.

	Abstract
1	Introduction
2	Tests of the Foundations of Gravitation Theory
	2.1	The Einstein equivalence principle
	2.2	Theoretical frameworks for analyzing EEP
	2.3	EEP, particle physics, and the search for new interactions
3	Metric Theories of Gravity and the PPN Formalism
	3.1	Metric theories of gravity and the strong equivalence principle
	3.2	The parametrized post-Newtonian formalism
	3.3	Competing theories of gravity
4	Tests of Post-Newtonian Gravity
	4.1	Tests of the parameter $γ$
	4.2	The perihelion shift of Mercury
	4.3	Tests of the strong equivalence principle
	4.4	Other tests of post-Newtonian gravity
	4.5	Prospects for improved PPN parameter values
5	Strong Gravity and Gravitational Waves: Tests for the 21st Century
	5.1	Strong-field systems in general relativity
	5.2	Motion and gravitational radiation in general relativity: A history
	5.3	Compact binary systems in general relativity
	5.4	Compact binary systems in scalar–tensor theories
6	Stellar System Tests of Gravitational Theory
	6.1	The binary pulsar and general relativity
	6.2	A zoo of binary pulsars
	6.3	Binary pulsars and alternative theories
	6.4	Binary pulsars and scalar–tensor gravity
7	Gravitational-Wave Tests of Gravitational Theory
	7.1	Gravitational-wave observatories
	7.2	Gravitational-wave amplitude and polarization
	7.3	Gravitational-wave phase evolution
	7.4	Speed of gravitational waves
8	Astrophysical and Cosmological Tests
9	Conclusions
	Acknowledgments
	References
	Footnotes
	Updates
	Figures
	Tables