This talk describes work on one of the first applications of algebra to theoretical computer science, the study of recursive program schemes. I would like to put a lot of the past work in perspective and then to describe recent work by Stefan Milius and myself which reworks the classical theory of uninterpreted and interpreted recursive program schemes using tools from coalgebraic recursion theory. Finally, I hope to speculate on whether the new work could be of interest to those pursuing AMAST’s goal of ”setting of software technology on a firm, mathematical basis.”