Starting with descriptions of rotational seismology, areas of interest and historical field measurements, the fundamental requirements for rotational seismometers for seismological and engineering application are formulated. On the above basis, a review of all existing rotational seismometers is presented with a description of the principles of their operation as well as possibilities to fulfill formulated requirements. This review includes mechanical, acoustical, electrochemical and optical devices and shows that the last of these types are the most promising. It is shown that optical rotational seismometer based on the ring-laser gyroscope concept is the best for seismological applications, whereas systems based on fiber-optic gyroscopes demonstrate parameters which are also required for engineering applications. Laboratory results of the Fibre-Optic System for Rotational Events & Phenomena Monitoring using a small 1-D shaking table modified to generate rotational excitations are presented. The harmonic and time-history tests demonstrate its usefulness for recording rotational motions with rates up to 0.25 rad/s.