The paper presents two new two-equation eddy-viscosity turbulence models for engineering applications, developed based on the author's extensive experience testing various turbulence models against a wide range of experimental data. The first model, the baseline (BSL) model, combines elements of the original $k-\omega$ model and the standard $k-\epsilon$ model, using the $k-\omega$ model in the inner region of the boundary layer and switching to the $k-\epsilon$ model in the outer region and free shear flows. This model avoids the strong freestream sensitivity of the $k-\omega$ model while maintaining its performance. The second model, the shear-stress transport (SST) model, modifies the definition of the eddy viscosity to account for the transport of the principal turbulent shear stress, leading to significant improvements in predicting adverse pressure gradient flows. The introduction highlights the discrepancies between the number of publications on two-equation models and the slow progress in accuracy, emphasizing the need for empirical approaches over theoretical concepts. The author discusses the limitations of existing models, such as the $k-\omega$ model's inability to predict the onset and amount of separation in adverse pressure gradient flows, and the lack of standardized criteria for measuring model improvement. The paper details the development of the BSL and SST models, explaining their mathematical formulations and the rationale behind the choices made. The BSL model is designed to retain the robustness of the $k-\omega$ model in the near-wall region while leveraging the freestream independence of the $k-\epsilon$ model in the outer part of the boundary layer. The SST model introduces a cross-diffusion term to account for the transport of the principal turbulent shear stress, improving the prediction of adverse pressure gradient flows. The results section compares the performance of the new models against the original $k-\omega$ and standard $k-\epsilon$ models in various flow scenarios, including flat plate boundary layers, free shear layers, adverse pressure gradient flows, backward-facing step flows, NACA 4412 airfoil flows, and transonic bump flows. The SST model consistently outperforms the others, particularly in predicting pressure-induced separation and viscous-inviscid interaction. The conclusions emphasize the empirical basis of the new models, their ability to avoid freestream dependency, and their superior performance in complex flows. The authors also highlight the flexibility and versatility of the models, which can be combined in various ways to suit different applications.The paper presents two new two-equation eddy-viscosity turbulence models for engineering applications, developed based on the author's extensive experience testing various turbulence models against a wide range of experimental data. The first model, the baseline (BSL) model, combines elements of the original $k-\omega$ model and the standard $k-\epsilon$ model, using the $k-\omega$ model in the inner region of the boundary layer and switching to the $k-\epsilon$ model in the outer region and free shear flows. This model avoids the strong freestream sensitivity of the $k-\omega$ model while maintaining its performance. The second model, the shear-stress transport (SST) model, modifies the definition of the eddy viscosity to account for the transport of the principal turbulent shear stress, leading to significant improvements in predicting adverse pressure gradient flows. The introduction highlights the discrepancies between the number of publications on two-equation models and the slow progress in accuracy, emphasizing the need for empirical approaches over theoretical concepts. The author discusses the limitations of existing models, such as the $k-\omega$ model's inability to predict the onset and amount of separation in adverse pressure gradient flows, and the lack of standardized criteria for measuring model improvement. The paper details the development of the BSL and SST models, explaining their mathematical formulations and the rationale behind the choices made. The BSL model is designed to retain the robustness of the $k-\omega$ model in the near-wall region while leveraging the freestream independence of the $k-\epsilon$ model in the outer part of the boundary layer. The SST model introduces a cross-diffusion term to account for the transport of the principal turbulent shear stress, improving the prediction of adverse pressure gradient flows. The results section compares the performance of the new models against the original $k-\omega$ and standard $k-\epsilon$ models in various flow scenarios, including flat plate boundary layers, free shear layers, adverse pressure gradient flows, backward-facing step flows, NACA 4412 airfoil flows, and transonic bump flows. The SST model consistently outperforms the others, particularly in predicting pressure-induced separation and viscous-inviscid interaction. The conclusions emphasize the empirical basis of the new models, their ability to avoid freestream dependency, and their superior performance in complex flows. The authors also highlight the flexibility and versatility of the models, which can be combined in various ways to suit different applications.