This review article discusses the modeling and interpretation of adsorption isotherms, focusing on various isotherm models used to analyze adsorption data. Adsorption isotherms are essential for understanding the mechanisms of adsorption processes and designing effective adsorption systems. The paper reviews the applications of different isotherm models, including linear and nonlinear regression analysis, and error functions for optimal data analysis. The article covers a range of isotherm models, including one-parameter models such as Henry's isotherm, Hill-Deboer model, Fowler-Guggenheim model, Langmuir isotherm, Freundlich isotherm, Dubinin-Radushkevich isotherm, Temkin isotherm, Flory-Huggins isotherm, Hill isotherm, Halsey isotherm, Harkin-Jura isotherm, and Jovanovic isotherm. It also discusses two-parameter models like Redlich-Peterson, Sips, Toth, Koble-Carrigan, Kahn, Radke-Prausnitz, and Langmuir-Freundlich isotherms. Additionally, it covers three-parameter models such as Fritz-Schlunder, Baudu, Weber-Van Vliet, and Marczewski-Jaroniec isotherms, as well as four-parameter and five-parameter isotherms. The paper emphasizes the importance of error analysis in evaluating the accuracy of isotherm models. It discusses various error functions, including the sum square of errors, hybrid fractional error function, average relative error, Marquardt's percent standard deviation, sum of absolute errors, sum of normalized errors, coefficient of determination, Spearman's correlation coefficient, and nonlinear chi-square test. These error functions help in comparing the performance of different isotherm models and determining the best fit for experimental data. The conclusion highlights the significance of accurate modeling and interpretation of adsorption isotherms in designing effective adsorption systems. It emphasizes the need to understand and clarify the usefulness of both linear and nonlinear regression analysis in various adsorption systems. The paper also notes the importance of using appropriate error functions to ensure the reliability of isotherm models in predicting adsorption behavior.This review article discusses the modeling and interpretation of adsorption isotherms, focusing on various isotherm models used to analyze adsorption data. Adsorption isotherms are essential for understanding the mechanisms of adsorption processes and designing effective adsorption systems. The paper reviews the applications of different isotherm models, including linear and nonlinear regression analysis, and error functions for optimal data analysis. The article covers a range of isotherm models, including one-parameter models such as Henry's isotherm, Hill-Deboer model, Fowler-Guggenheim model, Langmuir isotherm, Freundlich isotherm, Dubinin-Radushkevich isotherm, Temkin isotherm, Flory-Huggins isotherm, Hill isotherm, Halsey isotherm, Harkin-Jura isotherm, and Jovanovic isotherm. It also discusses two-parameter models like Redlich-Peterson, Sips, Toth, Koble-Carrigan, Kahn, Radke-Prausnitz, and Langmuir-Freundlich isotherms. Additionally, it covers three-parameter models such as Fritz-Schlunder, Baudu, Weber-Van Vliet, and Marczewski-Jaroniec isotherms, as well as four-parameter and five-parameter isotherms. The paper emphasizes the importance of error analysis in evaluating the accuracy of isotherm models. It discusses various error functions, including the sum square of errors, hybrid fractional error function, average relative error, Marquardt's percent standard deviation, sum of absolute errors, sum of normalized errors, coefficient of determination, Spearman's correlation coefficient, and nonlinear chi-square test. These error functions help in comparing the performance of different isotherm models and determining the best fit for experimental data. The conclusion highlights the significance of accurate modeling and interpretation of adsorption isotherms in designing effective adsorption systems. It emphasizes the need to understand and clarify the usefulness of both linear and nonlinear regression analysis in various adsorption systems. The paper also notes the importance of using appropriate error functions to ensure the reliability of isotherm models in predicting adsorption behavior.