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Ultrafast electron diffraction with bunch compression has reached a level of performance which allows for the accurate measurement of time-resolved diffuse scattering with a timeresolution of 150 femtoseconds. This information extends ultrafast electron diffraction to timeand momentum-resolved studies of phonon systems (lattice waves) in single-crystal materials. In this dissertation, time-resolved diffuse scattering is explored in two low-dimensional materials. First comes graphite, where anisotropic electron-phonon coupling and stiff phonon bands allow for maximum measurement contrast. The redundancy in ultrafast electron scattering patterns, as well as crystal symmetry, are used to robustly recover the occupancy of all in-plane phonon modes. The mode-, momentum-and time-dependent phonon populations reveal the nonequilibrium lattice states that follow photoexcitation and the complete breakdown of the two-temperature model often used to describe dynamics on the femtosecond time-scale. The measurements presented also provide a direct view of anharmonic decay pathways of phonons across the Brillouin zone, and a technique to extract electron-phonon coupling matrix elements fromphononpopulationisdeveloped. Thelessonsarethenappliedtofurtherourunderstanding of the best intrinsic thermoelectric materials, tin selenide. There, combined ultrafast electron diffraction and diffuse scattering measurements elucidate the mystery of ultralow thermal conductivity and high carrier mobility that gives tin selenide its high thermoelectric efficiency. It is found that strong and anisotropic electron-phonon coupling to polar modes dominates the …