Fast radio bursts (FRBs) are mysterious millisecond-duration astronomical radio transients with large dispersion measures in excess of the Galactic value. With a rapidly growing sample of FRBs, there are various interesting and valuable sciences are emerging. We show that the burst energy distribution has a power-law form which is very similar to the Gutenberg–Richter law of earthquake, while the aftershock sequence exhibits some local correlations. These findings suggest that the repeating FRB pulses may originate from the starquakes of a pulsar. Some newly discovered repeating FRBs, were reported to exhibit time–frequency downward drifting patterns. We propose a generic geometrical model to account for the observed downward drifting of sub-pulse frequency, within the framework of coherent curvature radiation by bunches of electron–positron pairs in the magnetosphere of a neutron star (NS). At last, we demonstrate that the first bright burst of FRB 171019 occurred during the merger event, while the subsequent repeating bursts are starquake-induced, and generally fainter, as the energy release rate for the starquakes can hardly exceed that of the catastrophic merger event.