Small-scale turbomachinery is increasingly used in carbon-free energy conversion systems, such as commercial or domestic scale heat pumps, fuels cells for transportation and waste heat recovery. The usage of aerodynamic bearings allows the design of compact compressors while guaranteeing a high degree of working fluid purity. Herringbone-grooved bearings have the advantages of oil-free operation, long-lifetime, high rotational speeds with relatively low frictional losses, no sealing requirements and avoidance of auxiliary systems. For the design of robust gas-bearing supported rotors accurate models are necessary and validated experimentally. Novel models for the herringbone grooved journal bearing (HGJB) are developed and used for comparison with the simplified narrow groove theory (NGT). A novel finite groove approach (FGA) is introduced for HGJB with rotating grooves, which spatially resolves the rotating grooves and offers a computation time speed-up of order 2, compared to the transient analysis. Good agreement between the FGA and the NGT is found for groove angles beta<35deg. For beta>35deg and compressibility numbers of Lambda>20, large discrepancies are reported, which are explained by increased compressibility effects, which are considered by the FGA but not by the NGT. In order to speed up computation time bearing meta-models are derived, enabling multidimensional regression by applying large scale vectorized computation. Artificial neural networks (ANN) are applied for modeling the highly non-linear multi-degrees of freedom solution parameter space of HGJBs static and linearized dynamic reaction forces. With the developed ANNs, speed-up factors of >10^5 for the static forces and >10^3 for the linearized dynamic reaction forces are achieved. A comparison between solving the partial differential equations directly and using the ANNs in combination with a rotordynamic system analysis shows a relative difference of <1.1%. The bearing models are integrated in a rotordynamic system and three different rotordynamic modules are introduced: (1) the transient state space approach, which solves the equations of motion and the thin-film lubrication equation simultaneously in time, (2) the linearized stability method and (3) a quasi-linear unbalance module. Non-dimensional rotordynamic stability maps are introduced. Systematic comparison between the models shows a difference of <7% in predicting the stability threshold for the linearized concentric analysis and differences of <8% in predicting orbital motions with amplitudes of epsilon=0.7 for the quasi-linear unbalance approach. Significant computation time speed-up of order 4 is obtained with the linearized forced response analysis compared to the transient approach. The rotordynamic modules with their integrated bearing models are validated experimentally, and the forced response and stability predictions are investigated. Good agreement was observed throughout the tested rotor configurations and unbalance scenarios for compressibility numbers of up to 42 between numerical predictions and experiments with a maximum difference of 19% at the largest measured orbital motion. In terms of stability, a prediction accuracy of the onset speed of sub-synchronous motion with a maximum error of 1.4% for nominal conditions was found by the linearized method.