By virtue of its simple structure, high operating speed and scalability, the resistive memory or RRAM is deemed a promising alternative to the charge-based memory, which is now facing severe scaling challenges. Of particular interest is the HfO 2 RRAM due to its immediate compatibility with mainstream integrated-circuit technology. A major problem is, however, the relatively high switching current.Currents on the order of 10 -3 A are typically observed in large-area cells (~10 -8 cm 2 ).In a recent work, a substantial reduction of the switching current to ~10 -5 A was achieved by scaling the cell area down to 100 nm 2 .Since one of the main strengths of RRAM is scalability, a further reduction of the switching current is deemed necessary in order to make ultra-high density memory application viable. At present, it is unclear to what extent could the switching current be reduced with cell area scaling. To address this question, resistance switching in HfO 2 is examined using a conductive atomic force microscope (C-AFM) and scanning tunneling microscope (STM) in this thesis. The excellent spatial resolution of C-AFM and STM enables the electrical properties of a thin dielectric to be probed over an extremely localized region. Through the C-AFM/STM technique, in this thesis, we examined resistance switching in a 4-nm thick HfO 2 , within a region of ~2 nm in diameter and achieved an ultra-low current switching capability. Furthermore, the unique abrupt reset behavior is observed in nanoscale RRAM with nanometer-level conducting filament (CF), on the contrary, the gradual current reduction trend is typically observed during the reset process in relatively large area