Nanostructures (NSs), including nanocrystals (NCs), nanowires (NWs), and nanosheets, are composed of inorganic cores with size <100 nm in at least one dimension. Their electronic structure and properties can be tailored by size and shape. NSs can serve as building blocks to create functional NS assemblies, with coupling from weak to strong by controlling the interparticle distance. In strongly coupled NC assemblies, properties emerge from collective interactions and offer great opportunities for designing materials with properties inaccessible in materials ‘on the shelf’. For semiconductors NSs with applications in electronics and optoelectronics, it is important to understand the behavior of carrier statistics and transport. In this thesis, we first use NWs, rather than NCs, to avoid inter-NC barriers and investigate the efficiency of doping and thus charge carrier statistics in NSs through measurements of charge transport in the platform of the field-effect transistors (FET). We show the doping efficiency of n- or p-doped PbSe NWs is increased as the permittivity of the surrounding environment increases and develop a theoretical model that agrees with our experimental data for both NW array and single NW devices. Then we investigate carrier transport in epitaxially-fused, CdSe NC arrays with wide necks between neighboring NCs synthesized by a cation exchange (CE) reaction from PbSe NCs through an intermediate. Time-resolved microwave conductivity measurements probe carrier transport at nanometer length scales and show a photoconductance of 0.28 cm2 V-1 s-1, the highest among CdSe NC solids reported with little or no necking. FET measurements probe carrier transport at micron length scales and realize high electron mobility of 35(3) cm2 V-1 s-1 with on-off ratios of 106 after doping. Last, we show that residual Pb impurities from CE reactions have detrimental effects on device turn-on, hysteresis, electrical stability, and carrier transport of CE-obtained CdSe NC films. The selection and surface functionalization of the gate oxide layer and low-temperature atomic-layer deposition encapsulation can suppress these detrimental effects. By converting the NC thin films layer-upon-layer, impurities are driven away from the gate-oxide interface and mobilities increase by 10 times.