This work addresses the problem of extracting 3D anatomical point landmarks from 3D tomographic images. Such image features are useful for a variety of 3D medical image analysis tasks, in particular for image registration, which is a key issue in clinical diagnosis and the planning of surgical interventions. In practice, landmarks are usually manually extracted from 3D images, which is tedious and time-consuming. Apart from that, up to now only a few local (differential) approaches to (semi-)automatic 3D point landmark detection have been proposed. We present new semi-automatic approaches to landmark detection and localization, where our focus is on point landmarks of the human head. After giving a comprehensive survey of the existing local approaches, we present in the first part new differential approaches to refined landmark localization as well as to the reduction of false detections. Our experimental studies show that compared to existing approaches, the localization accuracy as well as the detection performance are significantly improved. Moreover, we present the results of an extensive validation study in which we compare the performance of semi-automatic with that of (standard) manual landmark extraction. In the second part, we consider the extension of the local approaches to a new semi-global approach based on deformable models. In summary, the combination of the new semi-global approach with a local approach further improves both the localization accuracy and the detection performance.