Thermal transport in silicon nanostructures has captured the attention of scientists for understanding phonon transport at the nanoscale, and the competitive thermoelectric figure-of-merit has inspired engineers to develop efficient power generation and solid-state cooling devices. Firstly, our work focuses on identifying fundamental mechanisms of thermal transport in silicon nanostructures. The thermal transport interpretation remains unclear at the nanoscale and is often called into doubt due to the coupled effects of phonon coherence, boundary scattering, backscattering, and contact resistance. We isolate the wave-related coherence effects by comparing periodic and aperiodic nanomeshes, and quantify the particle-related backscattering effect by comparing variable-pitch nanomeshes. The lithographically-patterned silicon nanomeshes provide a unique opportunity for this progress because the relevant dimensions including the artificial periodicity, pitch, and neck were independently controlled within a monolithic measurement device. We measure identical (within 6% uncertainty) thermal conductivities for periodic and aperiodic nanomeshes of the same average pitch, and reduced thermal conductivities for nanomeshes with smaller pitches. Our simulations based on a ray tracing technique support the measurement results. We conclude phonon coherence is unimportant for thermal transport in silicon nanomeshes with periodicities of 100 nm and higher and temperatures above 14 K. In other words, the wave nature of phonons does not need to be considered to describe transport in the regime where periodicities are greater than the dominant wavelengths but smaller than inelastic mean free paths. We also show that phonon backscattering, as manifested in the classical size effect, is responsible for the thermal conductivity reduction in silicon nanomeshes. This work provides valuable insights for describing phonon transport in complex nanostructured geometries and improves a fundamental understanding of nanoscale thermal transport that is critical for a broad range of semiconductor technologies. Lastly, our work provides a novel thermal management design based on holey silicon, in which nanoscopic holes are lithographically patterned and vertical trenches are formed to offer tunable transport properties. Due to the unique thermal conductivity anisotropy including the low in-plane thermal conductivity and the high cross-plane thermal conductivity preserved by long-wavelength phonons, the holey silicon structure will provide innovative thermoelectric cooling performance even at a confined lateral space, which is unachievable by conventional isotropic materials. The thermal conductivity anisotropy is attractive for lateral thermoelectric cooling designs because the low in-plane thermal conductivity sets required temperature gradients for thermoelectric Peltier effects in the lateral direction and the high cross-plane conductivity enables effective heat dissipation from the hotspot in the vertical direction. This work investigates the role of thermal conductivity anisotropy in thermoelectric cooling through theoretical, numerical, and experimental approaches. The work bridges the gap between fundamental thermal sciences and device engineering, in which the holey silicon-based thermoelectric cooling device benefits from the unique transport phenomena at the nanoscale. The outcomes of this research present the anisotropic silicon nanostructures as efficient and effective thermoelectric materials that can offer transformative solutions to thermal management of nanoscale electronics.