Compact model plays an important role in designing integrated circuits and serves as a bridge to share the information between foundries and circuit designers. Since various flavors of transistor architectures like FDSOIs and FinFETs are proposed to improve device performances, the accurate, fast, and robust compact models, which are capable of reproducing the very complicated transistor characteristics like transconductance, are urgently required. Novel device concept, such as tunnel FETs (TFETs) and negative capacitance FETs (NCFETs), needs new device modeling methodology and understanding of device physics. In addition to transistors, memory device like magnetic tunnel junction (MTJ) compact model is also crucial for circuit designs. This dissertation presented the advanced research on compact models for the state-of-the art transistor and memory technologies: FDSOIs, FinFETs, TFETs, NCFETs, and MTJs. Due to the limitations in the aggressively scaled planar transistors, the devices with good electrostatic control are discussed and modeled into the industry standard model: BSIM-IMG for FDSOIs and BSIM-CMG for multi-gate FETs. Although the dynamic back-gate bias change help reduce the static power in FDSOIs, the leakages, overlap capacitance, and carrier transport are thus showing back-gate bias-dependence. The enhanced gate-related leakage, overlap capacitance, and mobility compact models are validated against the silicon data and incorporated into BSIM-IMG. The leakages through subsurface path and source-to-drain direct tunneling due to extremely short channel are also included in this work, which are in excellent agreement with the technology computer-aided design (TCAD) and atomistic simulations. The computationally efficiency of these models are the key solutions for evaluating the circuit performance of future technology nodes. Two paradigms of steep subthreshold slope transistors: TFETs and NCFETs as the promising candidates for future Internet of Things (IoT) and logic/analog applications are also presented in this thesis. TFET has a gated p-i-n diode structure, where the current relies on direct band-to-band tunneling in source/channel junction. Such tunneling mechanism breaks the tradition limitation of MOSFET turn-ON characteristics called the Boltzmann tyranny. The improvements in power consumption and delay of circuits are thus the emphasis and attention of device community, where the need of TFET compact model is fulfilled with the developed model in this work. NCFET is rapidly emerging as a preferred replacement for traditional MOSFET since the recent discovery of ferroelectric (FE) materials to amplify the voltage suggests that further scaling supply voltage is possible with the CMOS-compatible fabrication process of NCFET. The short channel effect, ferroelectric variability, and spacer optimization design are the focus in this thesis. The compact model of NCFET is improved to be more predictive for ferroelectric properties with verification against TCAD simulations. Monte-Carlo method is carried out in FE variability study, where the main finding is that the dielectric phase is critical but fortunately is theoretically possible to be absent. The spacer design reveals that further engineering the capacitance matching via parasitic capacitance is the key solution for future technology nodes. In addition to transistor compact models and physics, the memory device: spin-transfer-torque magnetic tunnel junction (STT-MTJ) is also presented. The resistances and critical currents are derived from the Landau-Lifshitz-Gilbert (LLG) equation and modeled analytically. The RC sub-circuit is found to describe the dynamic switching behavior of MTJ due to the precession and thermal fluctuation. The proposed MTJ compact model has been validated with silicon data from the industry and is capable of simulating a memory circuit with previously mentioned BSIM models.