Light-pulse atom interferometers (LAIs) have been applied for measurements of, e.g., local gravity, the gravity gradient, or the Sagnac effect with state-of-the-art sensitivities. We will present high-precision studies of the foundations of physics based on atom interferometry: A LAI has been used for testing the Lorentz invariance of gravity at part per billion (ppb) resolution, competitive with the best solar-system studies; measurements of the ratio of the Planck constant to the atom mass h/m, the fine structure constant a, and the Avogradro constant NA have so far reached about 3 ppb of precision, and sub-ppb sensitivities are within reach. Moreover, atom interferometers have recently been shown to yield an accuracy of 7×10-9 in measuring the gravitational redshift, a central prediction of general relativity: This effect has before been measured using clocks on a tower, aircraft, and a rocket, currently reaching a precision of 7×10-5.
Recent advances include matter wave beam splitters that transfer the momentum of up to n=24 photons, increasing the sensitivity of LAIs by a factor of n or n2; using hundreds of photons seems within reach. Cancelling the effects of vibrations has lead to a 2,500-fold gain in sensitivity. LAIs using increased interaction times, advanced algorithms for data analysis, higher atomic densities, and noise reduction to below the standard quantum limit are being developed. These advances will allow us to test the universality of free fall, another foundation of general relativity. Use of nuclei that are quite unlike each other (Cesium and Lithium) will help reaching competitive sensitivity. Furthermore, we discuss why LAIs appear promising as detectors for gravitational waves in the mHz - Hz frequency band, which is complementary to planned optical interferometers, such as LIGO and LISA.