Common Lisp is a towering language that supports a plethora of functionality useful for both scientific and mathematical programming. However---except for a few notable systems such as Axiom, Macsyma/Maxima, and ACL2---Lisp has not taken center stage for such kinds of programming tasks. We will analyze exiting systems, including computer algebra systems, technical computing systems, and other programming languages, and their utility in scientific and mathematical programming. Such a discussion will form a foundation for comparative study.Following that, we will expound on some features of Lisp that augment the expressiveness, simplicity, and utility of programs written in the language. In particular, we do so by way of three carefully selected pragmatic examples arising in fields ranging from the theory of special functions to numerical simulation.