Nanostructures are nanometer scale structures (characteristic length less than 100 nm) such as nanowires, ultra-small junctions, etc. Since nanostructures are less stable, their characteristic volume is much smaller compared to defect sizes and their characteristic length is close to acoustical phonon wavelength. Moreover, because nanostructures include significantly fewer charge carriers than microscale structures, electronic noise in nanostructures is enhanced compared to microscale structures. Additionally, in microprocessors, due to the small gate capacitance and reduced noise margin (due to reduced supply voltage to keep the electrical field at a reasonable level), the electronic noise results in bit errors. On the other hand, the enhanced noise is useful for advanced sensing applications which are called fluctuation-enhanced sensing. In this dissertation, we first survey our earlier results about the limitation of noise posed on specific nano processors. Here, single electron logic is considered for voltage controlled logic with thermal excitations and generic shot noise is considered for current-controlled logic. Secondly, we discuss our recent results on the electronic noise in nanoscale sensors for SEnsing of Phage-Triggered Ion Cascade (SEPTIC, for instant bacterial detection) and for silicon nanowires for viral sensing. In the sensing of the phage-triggered ion cascade sensor, bacteriophage-infected bacteria release potassium ions and move randomly at the same time; therefore, electronic noise (i.e., stochastic signals) are generated. As an advanced model, the electrophoretic effect in the SEPTIC sensor is discussed. In the viral sensor, since the combination of the analyte and a specific receptor located at the surface of the silicon nanowire occurs randomly in space and time, a stochastic signal is obtained. A mathematical model for a pH silicon nanowire nanosensor is developed and the size quantization effect in the nanosensor is also discussed. The calculation results are in excellent agreement with the experimental results in the literature.