Face presentation attacks are becoming more efficient since new 3D facial masks are used. Passive terahertz imaging offers specific physical properties that may improve presentation attack detection capabilities. The non-zero transmission capability through a variety of non-metallic materials may provide necessary information for presentation attack detection. The aim of this paper is to present outcomes of a study on face presentation attack detection using passive imaging at 250 GHz. An analysis of presentation attacks for facial recognition systems using custom displayed and printed photographs, 3D-printed and full-face flexible 3D-latex masks, is provided together with spectral characterization of various presentation attack instruments. A set of experiments with various instruments and various sets of clothing is described and discussed. Finally, two presentation attack detection methods are proposed. The first method is based on a threshold corresponding to a difference between mean intensities of selected regions of interests while the second method uses eight different deep learning classifiers to detect presentation attacks. Results of two validation schemes are presented.