A single-state grating echo interferometer offers unique advantages for time-domain studies of light-matter interactions using laser-cooled atoms, including applications that involve precision measurements of atomic recoil, rotation, and gravitational acceleration. To illustrate the underlying physics, we first discuss the output signal of the interferometer in the absence of spontaneous emission. The influence of spontaneous emission, magnetic sublevels, and the spatial profile of excitations beams on matter wave interference in a two-pulse interferometer is described, followed by a discussion of transit time limited experiments using a multipulse technique that offers several advantages. We also examine the enhancement in signal size achieved by a lattice interferometer. The sensitivity of the interferometer to magnetic gradients and gravitational acceleration is discussed along with extensions to frequency-domain studies of atomic recoil and rotation. Applications of coherent transient effects and echo techniques associated with internal state labeled interferometers that utilize magnetic sublevels of a single hyperfine state are considered for precise measurements of magnetic interactions such as atomic g-factor ratios. The article concludes with an overview of the suitability of the traditional two-pulse photon echo technique for measurements of atomic lifetimes and studies of superradiant emission in laser-cooled samples.