The physics-inspired HEMT modeling approach reported focuses on circuit design. Accuracy, speed and flexibility have decreased design cycle times with proven application to GaN technology. The flexibility of the single channel, scalable model has facilitated significant advances in microwave and mm-wave circuit designs. Replacing measurement with simulation, including load-pull, has proven to be viable, eliminating any reluctance to be creative in the design phase. Designers confidently evaluate alternative bias conditions and device geometries, source via and gate finger arrangements. Only one comprehensive empirical model is called upon for all aspects of circuit operation, which speeds up design time. To achieve this, even for GaN, the salient physics underpinning each of the many device characteristics and dependencies is captured within an efficient empirical formulation. The formulation is based on the two-region architecture comprising an accurate pre-saturation mode essential for switch and mixer applications, and a saturation mode similar to a virtual source. Displacement current and charge partitioning is based on mean weighted energy instead of a simple average, which significantly improves small-signal integrity and provides an inherent noise formulation. Large-signal descriptions include breakdown, leakage, and memory effects, so that load-pull, power and efficiency simulations are accurate. Small-signal derivatives, nonlinearity, and noise characteristics are correct at all quiescent, memory, and temperature, so that small-signal receiver elements are designed with the same large-signal model. Temperature and trapping, which epitomize the challenge for GaN, are implemented across the entire frequency domain with correct dependence on rates with bias and power. The characterization approach easily handles the demanding memory effects, power, voltages, and temperatures exhibited by GaN. Only one representative device is required to characterize a foundry process because the model extrapolates throughout the bias, power, and frequency space. Models for any geometry, number of fingers, or width, are synthesized from a scaled channel model. Successful designs at extreme frequencies and power levels have come from a single model characterized from a small sample device by fitting measurements at low frequencies and moderate bias. This lecture describes the modeling approach developed over the last two decades and how a correct physics underpinning offers scaling and statistical modeling and eased the move to GaN technology.