Many of the surfaces required today, and in the future, in high added value products can have any designed shape and often no axis of rotation. These complex geometrical surface shapes are termed freeform surfaces. In most cases, these surfaces are required to have sub-micrometer form accuracy and nanometric surface topography. This paper introduces some new and novel concepts to classify and evaluate freeform surfaces, including a structured neighbourhood signature fitting method for smooth freeform surfaces and a tessellation technique to identify and characterise micro-structured surfaces. Examples will be used throughout the paper to illustrate these new concepts.