This work investigates the electronic properties of very small gold and semiconductor particles using Scanning Tunneling Microscopy/Spectroscopy (STM/STS) and Ballistic Electron Emission Spectroscopy (BEES). Complementary theoretical works were also performed. The first theoretical work was to calculate the quantized states in the CdS/HgS/CdS quantum-well-quantum-dot nanocrystals. An eight-band envelope function method was applied to this system. This method treats exactly the coupling between the conduction bands, the light-hole bands, the heavy-hole bands, and the spin-orbit split bands. The contributions of all other bands were taken into account using second order perturbation theory. Gold nanocrystals with diameters of 1.5 nm have discrete energy levels with energy spacings of about 0.2 eV. These values are comparable to the single electron charging energy, which was about 0.5 eV in our experimental configuration. Since bulk gold doesnt have an energy gap, we expect the electron levels both below and above the Fermi level should be involved in the tunneling. Measured spectroscopy data have rich features. In order to understand and relate these features to the electronic properties of the nanocrystals, we developed a tunneling model. This model includes the effect of excited states that have electron-hole pairs. The relaxation between discrete electron energy levels can also be included in this model. We also considered how the nanocrystals affect the BEES current. In this work an ultra-high vacuum and low-temperature STM was re-designed and rebuilt. The BEEM/BEES capabilities were incorporated into the STM. We used this STM to image gold nanocrystals and semiconductor nanocrystals. STS and BEES spectra of gold nanocrystals were collected and compared with calculations.