The accelerating expansion of the universe is a major cosmological discovery, implying the presence of dark energy or a breakdown of Einstein's theory of gravity. This has led to extensive research to understand the origin of cosmic acceleration, with experiments aiming to measure expansion and structure growth with high precision. The paper reviews four key methods: Type Ia supernovae, baryon acoustic oscillations (BAO), weak gravitational lensing, and galaxy clusters. It discusses systematic uncertainties and strategies to control them for future dark energy missions like BigBOSS, LSST, Euclid, and WFIRST. Other methods, including redshift-space distortions and the Alcock-Paczynski effect, are also briefly reviewed. The paper presents forecasts for constraints on the dark energy equation of state and deviations from General Relativity using upcoming experiments. It emphasizes the value of a balanced program combining multiple methods to cross-check systematic uncertainties and leverage complementary information. Surveys probing cosmic acceleration provide data for various scientific investigations, continuing the tradition of mapping the universe in greater detail. The paper also discusses the history of cosmic acceleration, current theories, and future observational efforts, highlighting the importance of precise measurements to determine the nature of dark energy and the validity of General Relativity on cosmological scales.The accelerating expansion of the universe is a major cosmological discovery, implying the presence of dark energy or a breakdown of Einstein's theory of gravity. This has led to extensive research to understand the origin of cosmic acceleration, with experiments aiming to measure expansion and structure growth with high precision. The paper reviews four key methods: Type Ia supernovae, baryon acoustic oscillations (BAO), weak gravitational lensing, and galaxy clusters. It discusses systematic uncertainties and strategies to control them for future dark energy missions like BigBOSS, LSST, Euclid, and WFIRST. Other methods, including redshift-space distortions and the Alcock-Paczynski effect, are also briefly reviewed. The paper presents forecasts for constraints on the dark energy equation of state and deviations from General Relativity using upcoming experiments. It emphasizes the value of a balanced program combining multiple methods to cross-check systematic uncertainties and leverage complementary information. Surveys probing cosmic acceleration provide data for various scientific investigations, continuing the tradition of mapping the universe in greater detail. The paper also discusses the history of cosmic acceleration, current theories, and future observational efforts, highlighting the importance of precise measurements to determine the nature of dark energy and the validity of General Relativity on cosmological scales.