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The Blazhko phenomenon

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.