We report our recent analyses of the RR Lyrae Optical Gravitational Lensing Experiment (OGLE) photometry, which resulted in several new discoveries and important results. We present the in-depth analysis of the Blazhko effect discovered in several double-mode RR Lyr (RRd) stars for the first time. Typically, these stars show multiple modulation periods and somewhat atypical first overtone to fundamental mode period ratio. Our analysis of the Galactic bulge stars allowed a significant (~factor of 10) increase of the members of the recently detected group of double-mode radial-non-radial RR Lyr stars, pulsating in the first overtone and in an yet unidentified shorter period mode, with characteristic period ratio of the two modes around 0.61. With more than 200 new members of the group first statistical analysis of the group properties is possible. Finally, we report the discovery of an even more intriguing group of double-periodic RR Lyr stars. The dominant pulsation mode in these stars corresponds to the radial first overtone. The additional period is longer, the period ratios (first overtone to a period of an yet unidentified origin) tightly cluster around 0.686. Hence the additional period is longer than the unseen fundamental mode and cannot correspond to a purely acoustic pulsation mode.