Research discovery of ferroelectricity in doped hafnium dioxide thin films has ignited tremendous activity in exploration of ferroelectric FETs for a range of applications from logic to embedded memory to in-memory compute kernels. In this invite paper, we will present important highlights in the development of nonvolatile circuits and system design and optimization using FEFETs. We will begin with low-power Boolean logic implementations using steep-slope in reducing energy consumption with FeFETs. Nonvolatile memory and memory-logic-fusion circuits based on FeFETs provide further improvement in energy-efficiency solutions for extremely energy constrained applications. Specifically, we will focus on design and implementation of nonvolatile flip-flop design based on FeFETs, showing fJ-level backup and wakeup energy with ns-level speed. We will also discuss nonvolatile SRAM design based on FeFETs using 6T SRAM as the normal-mode operating cell and the 4T FeFET-based data backup circuitry. We will end with a discussion of FEFETs as an analog multi-state storage and local processing unit, for implementing in-memory compute kernels. The challenges and benefit of using FeFETs as in-memory processing units to accelerate hardware learning for deep neural networks will be elucidated.