Abstract This chapter proposes some new methods for computing empirical semivariograms and covariances and for fitting semivariogram and covariance models to empirical data. Grid-based empirical semivariograms and covariances are described, in which the grid values are smoothed using triangular kernels. A model-fitting procedure using modified iterative weighted least squares is presented. This algorithm is shown to be reliable for a wide range of data types and conditions, and its implementation in commercial software is discussed. Comparisons to restricted maximum likelihood estimation are also discussed.