The chapter discusses the method of weighted least squares as an appropriate approach for fitting variogram models in geostatistical studies. The weighting scheme gives more importance to early lags and downweights those with fewer pairs, even though the weights are derived under the assumption of Gaussian data. The method of generalized least squares, which accounts for correlation between variogram estimators at different lags, offers greater statistical efficiency but is more complex. The robust estimator based on square root differences is less of a compromise. The chapter also highlights the role of statistics in geostatistical studies, including data summarization, nonstationarity detection, variogram estimation, resource estimation, and reserve assessment. It emphasizes the importance of robust estimation techniques, particularly in the presence of contaminated data, and provides a detailed discussion on the assumptions and methods used in variogram fitting.The chapter discusses the method of weighted least squares as an appropriate approach for fitting variogram models in geostatistical studies. The weighting scheme gives more importance to early lags and downweights those with fewer pairs, even though the weights are derived under the assumption of Gaussian data. The method of generalized least squares, which accounts for correlation between variogram estimators at different lags, offers greater statistical efficiency but is more complex. The robust estimator based on square root differences is less of a compromise. The chapter also highlights the role of statistics in geostatistical studies, including data summarization, nonstationarity detection, variogram estimation, resource estimation, and reserve assessment. It emphasizes the importance of robust estimation techniques, particularly in the presence of contaminated data, and provides a detailed discussion on the assumptions and methods used in variogram fitting.