Rotational seismology is an emerging field for studying all aspects of rotational ground motions induced by earthquakes, explosions, and ambient vibrations. It is of interest to a wide range of geophysical disciplines, including strong-motion seismology, broadband seismology, earthquake engineering, earthquake physics, seismic instrumentation, seismic hazards, seismotectonics, and geodesy, as well as to physicists using Earth-based observatories for detecting gravitational waves generated by astronomical sources (predicted by Einstein in 1916). In this introduction to the BSSA special issue on rotational seismology and engineering applications, we will include (1) some background information, (2) a summary of the recent events that led to this special issue, and (3) an overview of its 51 papers-27 articles, 11 short notes, 4 reviews, 6 tutorials, and 3 supplementary articles. Our comments on these 51 papers are very brief and give just a hint of what the papers are about.Papers in this special issue demonstrate that earthquake monitoring cannot be limited to measuring only the three components of translational motion. We also need to simultaneously measure the three components of rotational motion and the many components of strains. A golden opportunity to improve our understanding of earthquakes lies in the near field of large earthquakes (within about 25 km of the earthquake ruptures), where nonlinear rock and soil response influences ground motions in a complicated way. Some Background InformationRotational effects of earthquake waves together with rotations caused by soil-structure interaction (e.g., in chimneys, monuments, or tombstones rotated on their supports) have been observed for centuries. A few early authors proposed rotational waves or at least some vortical motions. Some of these early observations, however, might have resulted from ground rocking caused by soil-structure interaction. Some early seismic instruments designed to detect and to record earthquake shaking also included the rocking of ground motion because it was believed that earthquakes were caused by explosions in the Earth (Trifunac, 2008). As summarized by Ferrari (2006), two models of an electrical seismograph with sliding smoked paper were developed by P. Filippo Cecchi (1822-1887) to record three-component translation motions and also the torsion movements from earthquakes. Although these instruments operated for several years, no rotational motion could be recorded because of low transducer sensitivity.Mallet (1862) proposed that rotations of a body on the Earth's surface are due to a sequence of different seismic phases emerging under different angles. Reid (1910) studied this phenomenon, which was observed in the 1906 San Francisco earthquake, and pointed out that the observed rotations are too large to be produced by waves of elastic distortion. Such waves "produce very small rotations, whose maximum amount, … is given by the expression 2πA=λ, where A is the amplitude and λ the wave-length; with a wave as short as 10...