  In spite of the accumulating high quality data on RR Lyrae stars, the
underlying cause of the (quasi)periodic light curve modulation (the so-called
Blazhko effect) of these objects remains as mysterious as it was more than
hundred years ago when the first RR Lyrae observations were made. In this
review we briefly summarize the current observational status of the Blazhko
stars, discuss the failure of all currently available ideas attempting to
explain the Blazhko effect and finally, we contemplate on various avenues,
including massive 2-3D modeling to make progress. Somewhat unconventionally to
a review, we present some new results, including the estimate of the true
incidence rate of the fundamental mode Blazhko stars in the Large Magellanic
Cloud, and tests concerning the effect of the aspect angle on the observed
distribution of the modulation amplitudes for Blazhko models involving
nonradial modes.
