Synthetic biology is a rapidly developing field that aims to engineer new biological systems that do not already exist in Nature or redesign existing systems from scratch. The emergence of synthetic biology has been supported by a number of enabling technologies and what has developed is a broad field that currently encompasses many activities. The aim of this chapter is to introduce the field and discuss some key examples to date. What these examples have in common is a set of underlying molecular biology techniques including DNA assembly and combinatorial diversity generation, as well as computational modelling to assist in designing the new biological systems.