The von Neumann model of computing has formed the basis of virtually all of the "traditional" programming languages such as Fortran, C, Pascal, Cobol, Ada, etc. The goal of the course is to introduce the student to a number of the latest developments in alternatives to the von Neumman model, and describe some of the more significant languages which have been derived from them. Understanding these developments will involve a four step process. First, the fundamental mathematics behind the computational models will be reviewed. Then we will introduce the key abstract machines that mechanize this mathematics into a computational model, and provide the common semantics for languages of each class. Third, we will introduce the "prototypical" programming language fro that class (Lisp, Prolog, and Smalltalk), and how the syntax of these languages permit direct specification of the kinds of computational steps provided in the abstract machines. This includes compilers and interpreters, especially self-interpreters. Finally, we will survey other common languages in each class, architectures of real machines that were optimized for them, and unique capabilities offered by them, such as true and very natural parallelism.