We discuss the role of linear models for two extrapolation problems. The rst is the ex-trapolation to the limit of innite series, i.e. convergence acceleration. The second is an extension problem: Given function values on a domain $D_0$, possibly with noise, we would like to extend the function to a larger domain $D, D_0 \subset D$.  In addition to smoothness at the boundary of $D_0$, the extension on $D \ D_0$ should also resemble behavioral trends of the function on $D_0$, such as growth and decay or even oscillations. In both problems we discuss the univariate and the bivariate cases, and emphasize the role of linear models with varying coefficients.