A spatial analysis often involves manipulating and solving linear systems based on matrices derived from covariance functions. This talk will present several computational and modeling strategies for dealing with the matrix calculations when spatial data sets are large. Some of these approaches include iterative methods for solving large linear systems and inducing sparsity in the covariance matrix through tapering. As part of the theory for justifying tapering there is the tantalizing connection with kernel methods and some discussion will be given about equivalencs between classical spatial estimators and kernel smoothing.