In the last few years, various studies on terahertz (THz) birefringence have been presented, based on polarization-sensitive THz time-domain spectroscopy. The field of THz birefringence is a wide one covering several aspects, such as different materials exhibiting THz birefringence, polarization-sensitive THz technology, as well as numerous methods for extracting the birefringence properties of a sample from the THz data. Therefore, this paper aims at reviewing recent results on THz birefringence measurements presented in literature, addressing the above aspects and giving an overview of the topic. Moreover, it will focus on the investigation of birefringent fibrous samples, where specific results will be discussed in detail. Altogether, this paper should give a comprehensive view on the recent achievements in the measurements of THz birefringence.