As the demand for big data applications and faster computation increases, there is an ever-growing need for memory devices with high performance, low cost, and large storage density. Emerging Non-Volatile Memory (NVM) devices such as Phase Change Memory (PCM), Resistive Random Access Memory (RRAM), and Spin-Transfer-Torque Magnetic Random Access Memory (STT-MRAM) are promising candidates for the Storage Class Memory (SCM), which was proposed to be a new class of memory devices to fill the gap between Dynamic Random-Access Memory (DRAM) and storage memory. One of the advantages of NVM is the simple two-terminal device structure, allowing for the crossbar memory array with smallest 4F2 (F being the lithography feature size) footprint possible. However, such structure needs an access device at each crosspoint in order to reduce the so called “sneak path” effect. The CMOS transistor could serve as an access device but it requires 12 F2 area. Therefore, the transistor needs to be replaced by a two-terminal selector device that could be stacked on top of the memory element. Threshold switching devices appear to be the best candidate for selectors due to their extreme nonlinearity of I-V characteristic. However, the mechanism responsible for the threshold switching has not been well understood in many materials systems. This study focused on understanding the switching mechanism and its characterization in binary transition metal oxide-based devices. To understand the threshold switching behavior, I have started with VO2-based two-terminal planar devices. I developed an electrothermal model based on Joule heating to simulate the quasi-DC device I-V and transient response of the device under short pulses at various stage temperatures. The electrothermal model fully reproduced the I-V of VO2 devices in both OFF-state and ON-state, which allowed to follow the formation and evolution of the conductive filament within the device. The simulated dynamics of threshold switching agreed well with the experimentally measured data across 6 orders of magnitude. The good agreement between simulation and experimental results indicated temperature induced insulator to metal transition in VO2-based devices with no evidence of electronically-induced effects. Therefore, the threshold switching behavior in VO2-based devices can be explained by a more general Joule heating induced thermal runaway model. Furthermore, the electrothermal model was applied to TaOx-based threshold switches and successfully reproduced the S-shape threshold switching I-V characteristic due to thermal runaway mechanism. To experimentally discriminate the thermal-induced switching from other proposed mechanisms, I used Scanning Thermal Microscopy (SThM) and Scanning Joule Expansion Microscopy (SJEM), two scanning probe thermometry techniques to characterize the temperature profile and thermal expansion profile on the top surface of the TaOx-based devices. During the measurements, the devices were biased at several voltages below and up to the threshold voltage (VTH). The measurement showed that the temperature increase of 80 K was reached at VTH to cause the thermal runaway leading to threshold switching behavior. The measurement results experimentally supported the Joule heating induced thermal runaway as the mechanism of threshold switching in TaOx-based devices. By confirming the validity of the thermal-induced threshold switching behavior, I completed a comprehensive simulation study using the electrothermal model on the scaling behavior of three transition metal oxide (VO2, TaOx and NbO2) based selector devices with a vertical crossbar structure. The device characteristic was simulated as a function of device lateral size, oxide thickness, and stage temperature. The device performance, such as I-V characteristic, leakage current, filament size, and temperature in the ON-state were simulated and compared between devices with different dimensions and different materials. The benchmarking of one selector/one resistor (1S1R) cell using the scaled device characteristics with a set of parameters of a generic memory element was also evaluated. Further, the ideal material properties for selector application was calculated based on the figures of merit of the device performance.