A typical electronic or photonic device may consist of several materials each one potentially meeting at an interface or terminating with a free-surface boundary. As modern device dimensions reach deeper into the nanoscale regime, interfaces and boundaries become increasingly influential to both electrical and thermal energy transport. While a large majority of the device community focuses on the former, we focus here on the latter issue of thermal transport which is of great importance in implementing nanoscale devices as well as developing solutions for on-chip heat removal and waste heat scavenging. In this document we will discuss how modern performance enhancing techniques (strain, nanostructuring, alloying, etc.) affect thermal transport at boundaries and across interfaces through the avenue of three case studies. We use first-principles Density Functional Perturbation Theory to obtain the phonon spectrum of the materials of interest and then use the dispersion data as input to a phonon Boltzmann Transport model. First, we investigate the combined effects of strain and boundary scattering on the in-plane and cross-plane thermal conductivity of thin-film silicon and germanium. Second, we review a recently developed model for cross-dimensional (2D-3D) phonon transport and apply it to 3D-2D-3D stacked interfaces involving graphene and molybdenum disulfide 2D-layers. Third, we combine relevant models from earlier Chapters to study extrinsic effects, such as line edge roughness and substrate effects, on in-plane and through-plane thermal transport in 1H-phase transition metal dichalcogenide (TMD) alloys. Through these investigations we show that: (1) biaxial strain in Si and Ge thin-films can modulate cross-plane conductivity due to strong boundary scattering, (2) the thermal boundary conductance between 2D-3D materials can be enhanced in the presence of an encapsulating layer, and (3) the thermal conductivity of 1H-phase TMDs can be reduced by an order of magnitude through the combination of nanostructuring, alloying, and substrate effects.