Since the invention of cancer radiotherapy, its primary goal has been to maximize lethal radiation doses to the tumor volume while keeping the dose to surrounding healthy tissues at zero. Sadly, conventional radiation sources (γ or X rays, electrons) used for decades, including multiple or modulated beams, inevitably deposit the majority of their dose in front or behind the tumor, thus damaging healthy tissue and causing secondary cancers years after treatment. Even the most recent pioneering advances in costly proton or carbon ion therapies can not completely avoid dose buildup in front of the tumor volume. Here we show that this ultimate goal of radiotherapy is yet within our reach: Using intense ultra-short infrared laser pulses we can now deposit a very large energy dose at unprecedented microscopic dose rates (up to 1011 Gy/s) deep inside an adjustable, well-controlled macroscopic volume, without any dose deposit in front or behind the target volume. Our infrared laser pulses produce high density avalanches of low energy electrons via laser filamentation, a phenomenon that results in a spatial energy density and temporal dose rate that both exceed by orders of magnitude any values previously reported even for the most intense clinical radiotherapy systems. Moreover, we show that (i) the type of final damage and its mechanisms in aqueous media, at the molecular and biomolecular level, is comparable to that of conventional ionizing radiation, and (ii) at the tumor tissue level in an animal cancer model, the laser irradiation method shows clear therapeutic benefits.