Planets transiting their star can cross a starspot, and that — since the spot is dimmer than its surrounding — causes an upward blip in the light-curve of the transit. The same starspot can be occulted in consecutive transits, and so is seen later in phase each time because the star has rotated between the transits.
Keele University PhD student Teo Močnik has looked at the Kepler K2 lightcurve of Qatar-2, a star known to host a hot Jupiter in a 1.34-day orbit. The lightcurve records 59 consecutive transits over a 79-day period and Močnik finds that most of the observed transits are affected by starspots (link to paper).
In the plot below each numbered lightcurve is from a transit, which occurs between the vertical dashed lines. The transit profile itself, however, has been subtracted in order to better show the starspot features.
The starspots occur in groups, shown by red ellipses, and each group is the same starspot being seen in consecutive transits. Interestingly, though, the groups of spots themselves recur. Thus the starspots are lasting long enough that they pass behind the limb of the star, and then re-appear to be transited again one stellar rotation cycle later!
One particular starspot first causes the features in transits 20 to 22, then comes round again to produce the features in transits 33 to 36, and then comes round once again to produce the features in transits 46 to 50. Thus the starspot must have lasted for at least 40 days.
We thus have one of the best observations yet of a starspot on a star other than our sun. From this information we can calculate the rotation period of the star, place limits on the size, position and longevity of the spots, and also show that the planet’s orbit is closely aligned with the spin axis of the star.