This paper provides indoor reflection, scattering, transmission, and large-scale path loss measurements and models, which describe the main propagation mechanisms at millimeter wave and Terahertz frequencies. Channel properties for common building materials (drywall and clear glass) are carefully studied at 28, 73, and 140 GHz using a wideband sliding correlation based channel sounder system with rotatable narrow-beam horn antennas. Reflection coefficient is shown to linearly increase as the incident angle increases, and lower reflection loss (e.g., stronger reflections) are observed as frequencies increase for a given incident angle. Although backscatter from drywall is present at 28, 73, and 140 GHz, smooth surfaces (like drywall) are shown to be modeled as a simple reflected surface, since the scattered power is 20 dB or more below the reflected power over the measured range of frequency and angles. Partition loss tends to increase with frequency, but the amount of loss is material dependent. Both clear glass and drywall are shown to induce a depolarizing effect, which becomes more prominent as frequency increases. Indoor propagation measurements and large-scale indoor path loss models at 140 GHz are provided, revealing similar path loss exponent and shadow fading as observed at 28 and 73 GHz. The measurements and models in this paper can be used for future wireless system design and other applications within buildings for frequencies above 100 GHz.