Functional programming is a programming paradigm that was introduced by LISP. Many modern languages computational systems were inspired by LISP and one them is Mathematica.
It seems that the next biggest impact of functional programming is going to come from the application to parallel/distributed programming. One example of this emerging technology is the MapReduce framework developed by Google. In similar way, Yahoo is developing Haddop for the same purposes.
Another example is of course the implementation of WolframAlpha mostly developed in Mathematica.
There are many tutorials available including youtube videos such as
MapReduce Cluster Computing
One of the implementations that called my attention is MARS, which is developed on the top of CUDA.