The chapter discusses the calibration problem in various industries, focusing on both linear and non-linear models. Most models, particularly in chemical applications, use simple linear calibration techniques for instruments like pH meters and NIR instruments. Early work by Shukla (1972) highlighted the statistical dimensions of the problem, and it was recognized that non-linear models often require linear approximations. However, the goal remains to estimate the best possible non-linear function. Statistical calibration methods have been reviewed by Osborn (1991), and robust approaches are discussed by Kitso s and Muller (1995). For multivariate cases, Brown (1993), Bereton (2000), and Oman and Wax (1984) provide relevant references. Cross-validation is also mentioned as a method used in calibration problem development. The chapter introduces a simple regression model and the goal of estimating a nonlinear function of linear parameters. Two estimators, the classical predictor and the inverse predictor, are compared based on sample size and the ratio of variance to the slope. The classical predictor is shown to be more consistent and efficient under certain conditions. The main challenge in calibration is constructing confidence intervals due to the lack of variance for the estimated parameter. Optimal experimental design approaches, such as D-optimality and c-optimality, are discussed to address these difficulties. Bayesian and structural inference methods are also mentioned, with Bayesian methods often coinciding with the inverse regression when the sample size is small. Nonlinear calibration problems are approached using both classical and Bayesian methods, often based on Taylor expansions of the non-linear model. The chapter concludes by emphasizing the importance of linear approximations in nonlinear calibration.The chapter discusses the calibration problem in various industries, focusing on both linear and non-linear models. Most models, particularly in chemical applications, use simple linear calibration techniques for instruments like pH meters and NIR instruments. Early work by Shukla (1972) highlighted the statistical dimensions of the problem, and it was recognized that non-linear models often require linear approximations. However, the goal remains to estimate the best possible non-linear function. Statistical calibration methods have been reviewed by Osborn (1991), and robust approaches are discussed by Kitso s and Muller (1995). For multivariate cases, Brown (1993), Bereton (2000), and Oman and Wax (1984) provide relevant references. Cross-validation is also mentioned as a method used in calibration problem development. The chapter introduces a simple regression model and the goal of estimating a nonlinear function of linear parameters. Two estimators, the classical predictor and the inverse predictor, are compared based on sample size and the ratio of variance to the slope. The classical predictor is shown to be more consistent and efficient under certain conditions. The main challenge in calibration is constructing confidence intervals due to the lack of variance for the estimated parameter. Optimal experimental design approaches, such as D-optimality and c-optimality, are discussed to address these difficulties. Bayesian and structural inference methods are also mentioned, with Bayesian methods often coinciding with the inverse regression when the sample size is small. Nonlinear calibration problems are approached using both classical and Bayesian methods, often based on Taylor expansions of the non-linear model. The chapter concludes by emphasizing the importance of linear approximations in nonlinear calibration.