<p indent="0mm">On June 29, 2021, the LIGO, Virgo, and KAGRA collaboration published a paper to announce the detection of two neutron star-black hole (NS-BH) merger events GW200105 and GW200115 via gravitational waves (GWs). This unprecedented discovery is selected as one of the six surprising records science set in 2021 by <italic>Science News</italic>. The first event, GW200105, was caused by the merger of a <inline-formula id="INLINE14"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup other="0"><mml:mrow other="0"><mml:mn other="0">8.9</mml:mn></mml:mrow><mml:mrow other="1"><mml:mo other="1">−</mml:mo><mml:mn other="1">1.5</mml:mn></mml:mrow><mml:mrow other="1"><mml:mo other="1">+</mml:mo><mml:mn other="1">1.2</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> solar mass (<italic>M</italic><sub>sun</sub>) BH with a <inline-formula id="INLINE16"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup other="0"><mml:mrow other="0"><mml:mn other="0">1.9</mml:mn></mml:mrow><mml:mrow other="1"><mml:mo other="1">−</mml:mo><mml:mn other="1">0.2</mml:mn></mml:mrow><mml:mrow other="1"><mml:mo other="1">+</mml:mo><mml:mn other="1">0.3</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula><italic>M</italic><sub>sun</sub> NS at about 900 million light years away from Earth, and the second event, GW200115, was caused by the merger of a <inline-formula id="INLINE18"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup other="0"><mml:mrow other="0"><mml:mn other="0">5.7</mml:mn></mml:mrow><mml:mrow other="1"><mml:mo other="1">−</mml:mo><mml:mn other="1">2.1</mml:mn></mml:mrow><mml:mrow other="1"><mml:mo other="1">+</mml:mo><mml:mn other="1">1.8</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula><italic>M</italic><sub>sun</sub> BH and a <inline-formula id="INLINE20"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup other="0"><mml:mrow other="0"><mml:mn other="0">1.5</mml:mn></mml:mrow><mml:mrow other="1"><mml:mo other="1">−</mml:mo><mml:mn other="1">0.3</mml:mn></mml:mrow><mml:mrow other="1"><mml:mo other="1">+</mml:mo><mml:mn other="1">0.7</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula><italic>M</italic><sub>sun</sub> NS at about 1 billion light years away from Earth. The mass of the massive component in each of these two binaries, determined by the GW data, is larger than the minimum mass of all known astrophysical origin BHs (~5<italic>M</italic><sub>sun</sub>), thus it must be a BH, while the mass of the light one is less than the maximum mass but larger than the minimum mass of known NSs, thus it must be a NS. The detected GW waveform of each binary indicates some tidal deformation of the light component, which is also consistent with a NS nature of that component. The sky localizations of these two events are poorly determined by the GW waveforms, i.e., about 7200 and 600 square degrees for GW200105 and GW200115, respectively. NS-BH systems can be generated by different mechanisms, including the evolution of isolated binaries, the dynamical interactions in dense star clusters and young star clusters, and the star formation/evolution and interactions in the gaseous accretion disk around supermassive BHs in active galactic nuclei. The NS-BH merger rates resulting from different mechanisms may be different. The inferred NS-BH merger rate from the detection of GW200105 and GW200115 suggests that the dynamic origin in dense star clusters may be ruled out. Some NS-BH mergers may lead to electromagnetic radiation. If the BH component of a NS-BH merger is small, the NS may be tidally disrupted and an electromagnetic (EM) counterpart, i.e., a kilonova, emerges from the merger. The NS can be directly plunged into the BH without EM radiation, however, if the BH mass is significantly large. No EM counterpart was detected for the two NS-BH merger events. This could be due to that either no EM counterpart is generated from each merger, or the generated EM counterpart is too faint to be detected or simply missed by those telescopes searching for it. In addition, a NS-BH binary may be also directly discovered by monitoring the variation of the arrival time of pulsar pulses with radio telescopes, if the NS component is a pulsar. The detection of NS-BH systems can be used to not only constrain the evolution of (binary) stars and the nature of NS and BH, but also test the high mode GW radiation and the theory of gravity. In the future, GW and EM waves will inevitably detect a large number of NS-BH binaries and their mergers, which will be of great importance for investigating stellar physics, compact objects, gravity theory, and even cosmology.