The article comprises three main parts: a historical review on navigation, the mathematical basics for calculation and the clinical applications of navigation devices. Main historical steps are described from the first idea till the realisation of the frame-based and frameless navigation devices including robots. In particular the idea of robots can be traced back to the Iliad of Homer, the first testimony of European literature over 2500 years ago. In the second part the mathematical calculation of the mapping between the navigation and the image space is demonstrated, including different registration modalities and error estimations. The error of the navigation has to be divided into the technical error of the device calculating its own position in space, the registration error due to inaccuracies in the calculation of the transformation matrix between the navigation and the image space, and the application error caused additionally by anatomical shift of the brain structures during operation. In the third part the main clinical fields of application in modern neurosurgery are demonstrated, such as localisation of small intracranial lesions, skull-base surgery, intracerebral biopsies, intracranial endoscopy, functional neurosurgery and spinal navigation. At the end of the article some possible objections to navigation-aided surgery are discussed.