The MAGIC experiment was upgraded to a two-telescope system in 2009. Unlike other Imaging Air Cherenkov Telescope arrays, MAGIC has operated for five years exclusively in monoscopic mode, and the single telescope analysis was optimized throughout this time. To improve the analysis, we used techniques like the random forest event classification method for different purposes, and sophisticated image cleaning algorithms. The monoscopic performance was optimized in the energy domain around and below 100 GeV, which is inaccessible for the other arrays of Cherenkov telescopes. Still, with these analysis techniques, we were competitive also in the TeV regime. In the recent development of the stereoscopic analysis chain, the know-how of these single telescope techniques was combined with the new possibilities of the three-dimensional reconstruction, taking advantage both of the richness of single images and their projections onto the sky. We present recent advancements in the image cleaning and direction reconstruction algorithms, sky mapping and other procedures currently used in the analysis of MAGIC stereo data.