Two-dimensional (2D) inorganic materials present exciting opportunities for new scientific and technological breakthroughs. In this work, novel fabrication characterization and simulation techniques are presented for inorganic nanosheets and nanostructured thin films with the motivation of advancements in thermoelectrics, flexible electronics, optoelectronics and thermal engineering. Metal oxide nanosheet stacks of NaxCoO2 and KxCoO2.yH2O are fabricated using a novel bottom-up method based on sol-gel chemistry, E-field induced kinetic demixing and high temperature heat treatment. The nanosheet thicknesses can be 10- 100 nm while their lengths can measure up to 1.8 mm long. The stacked nanosheets are readily delaminated into very large (<350 [MICRO SIGN]m long, ~100 nm thick) free-standing 2D crystals. Both NaxCoO2 and KxCoO2.yH2O nanosheets are electrically conductive and show ductility. Thermoelectric efficiency of bulk NaxCoO2 is expected to improve in the nanosheet form due to phonon confinement and scattering. Novel p-type TCO thin films of Ca3Co4O9 nano-plates are produced using a sol-gel and spin coating based process. The process parameters can be varied to produce TCO thin films with sheet resistance as low as 5.7 kΩ/sq ([rho] [ALMOST EQUAL TO] 57 mΩ[MIDDLE DOT]cm) or with average visible range transparency as high as 67%. The FOM for the topperforming Ca3Co4O9 thin film (151 MΩ-1) is higher than FOM values reported in the literature for all other solution processed, p-type TCO thin films and higher than most others prepared by PVD and CVD. Frequency resolved phonon transport experiments are performed on nanofabricated Si nanosheets using micro-scale phonon spectrometry devices. Current work mainly focus on understanding the frequency resolved phonon transport measurement results using Monte Carlo (MC) simulations. These MC simulations assume that phonon transmission is dominated by phonon-surface interactions and use the well-known Ziman theory to predict phonon-surface scattering rates. Although, the MC model predicts a diffuse surface scattering probability of less than 40% for the measured surface roughness (1 nm), the measurements are consistent with a 100% probability. The nanosheets therefore exhibit the so-called 'Casimir limit' at a much lower frequency than expected if the phonon scattering rates follow the Ziman theory.