This note compares several different approaches to selecting an s-to-z mapping function for the purpose of converting a continuous-time transfer function F(s) to an "equivalent" discrete-time transfer function F(D)(z). The primary bases of comparison are stability and accuracy. Second bases of comparison include : 1) the amount of computation needed to process one input to produce one output, 2) the ease with which the coefficients of F(D)(z) can be determined, in particular, as the sampling period T is varied, 3) the ease of determining stability, in particular, the maximum value of T for stability, 4) the self-starting capability, and 5) compatibility with decomposition in the s-domain.