The machinability of a surface describes its ability to be machined and the factors which affect this. These are independent of any material properties or cutting parameters but instead reflect an ability to replicate a desired tool path motion with sufficient control of the material removal process. Without this control there is a potential for surface defects and costly finishing stages. Five-axis CNC milling machines are commonly used for machining complex free-form shapes. The processes required to obtain CNC instructions for a machine tool, starting from a target surface, are presented. An overview is first given and later formalised with mathematical methods. Specifically, a moving cutting tool is characterised by a tool path motion. Interpreting the moving cutter in terms of moving machine axes provides a diagnostic tool for detecting machining errors. Examination of two case studies reveals different types of errors, machine-dependent and machine-independent. The contribution of geometry to machine-independent errors is discussed and related back to the machinability of a surface.