There are many problems in demography involving the smoothing or interpolation of data. Usually a solution is obtained by fitting a polynomial or a suitable model curve. Often, however, fitting a spline proves to be a simple recourse. Splines were invented nearly 30 years ago and have been shown to have desirable properties. Although spline functions are by no means unknown to demographers, no simple and direct explanation of their application exists. We hope to remedy this deficiency with this expository piece.