Electrical and physical properties of low-dimensional structures have been studied for the various applications such as electronics, sensors, and etc. Low-frequency noise measurement is also a useful technique to give more information for the carrier dynamics correlated to the oxide traps, channel defects, and scattering. In this thesis, the electrical transport and low-frequency noise of low-dimensional structure devices such as multi-gate structures (e.g. FinFETs and Junctionless FETs), 3-D stacked Si/SiGe nanowire FETs, carbon nanotubes, and graphene are presented. From the view point of top-down and bottom-up approaches, the impacts of LF noise are investigated according to the dimensionality, conduction mechanism (surface or volume conduction), strain technique, and metal-semiconductor junctions.