Direct visualization of dynamic and non-equilibrium processes occurring on the atomic-scale remains a tremendous challenge owing to the condensed time-scales associated with the reduction in length-scale. Coherent phonon transport, for example, occurs at the speed of sound over distances spanning a few nanometers to a few microns. As such, a single wavefront may emanate, propagate, and scatter over the course of just a few picoseconds. Uniquely, ultrafast electron microscopy (UEM) has the ability to probe phonon transport processes on the relevant condensed time- and length-scales simultaneously, avoiding ensemble averaging over time and space characteristic of many traditional probes. Here, we have focused on the development of UEM as a tool for direct investigation of energy transport processes on the nanoscale. We have studied a variety of phenomena in two-dimensional atomic crystals and discussed progress in methodologies in operation of a thermionic UEM. In UEM, we call upon a variety of analytical modalities which utilize elastic scattering as a sensitive indicator of structural modulation within a crystalline lattice. Contrast in real-space arising from small angular perturbations in lattice orientation (and as result, local modulation of the Bragg condition) associated with phonon-mediated elastic deformation allows imaging the propagation of individual phonon wavefronts. We have discovered that phonon nucleation and launch occurs at discrete spatial locations along individual interfaces, and that the appearance of coherent, propagating wavefronts are extremely sensitive to the shapes of local strain fields and vacuum-crystal interfaces. Additional information from local elastic scattering in reciprocal-space allows examination of the specific modes and mechanisms of the observed phonon transport. In thin-films of WSe2, we conclude that the observed modes arise from interfacial stress resulting from the initial excitation and confinement of compressional waves along the WSe2 c-axis stacking direction within the thickness of the specimen. We also observe large-amplitude out-of-plane modes in single-crystal and polycrystalline monolayer graphene membranes through examination of laser-excited variation in the Debye-Waller factor; we expect the intrinsic ripples of the suspended membranes mediate flexural modes in a manner similar to the morphologically dependent wavefronts in WSe2. We have found that the ultrafast imaging and diffraction experiments are subject to a variety of practical challenges associated with stroboscopic operation. For one, heat dissipation from the specimen must be considered such that pseudo-steady-state operating temperatures resulting from the laser-pulse-trains are within ranges suitable for a particular experiment. Additionally, dynamics occurring on time-scales comparable to instrument response require precise deconvolution for proper interpretation of instrinsic material response. As such, we systematically optimize photoelectron generation and collection and map the space-charge and temporal instrument-response parameter space as a function of photoelectron-packet population. We obtain photoelectron packets populated by up to ~105 electrons, and instrument-response times range from 1 to 10 ps (FWHM) for laser-limited single-electron packets to those with maximum packet population. This large range of achievable bunch-charge increases experimental flexibility and allows UEM experiments to be conducted at relatively low repetition rates facilitating investigation of a greater range of ultrafast phenomena. We expect the methodology and insight presented in this work will aid in future quantitative studies of energy transport in crystalline materials with nanostructured interfaces and atomic defects. Ultimately, we envision the direct insight available in UEM will facilitate design of materials and structures for precise control of energy transport and improvement of the numerous applications in which understanding heat transport is critical.