Information processing is fundamental to life: metabolism, replication, evolution, etc all rely on it. Extant living systems carry out information processing chemically, using biochemistry. Chemistry-based computation is key to the information processing taking place in life. The most powerful, and yet simple, known construct in computation is the Turing machine. It consists of a finite state machine capable of giving unique responses to inputs from an infinite tape on which it can also write and erase. A Turing machine emulates a mathematician carrying out a mechanical repetitive computation on a sheet of paper. Can a computation be carried out with chemistry? Can it be done without biochemistry? In this talk I will discuss some of our recent experimental progress in answering these questions and illustrate it with the application to a common problem in computation theory.