Resistance switching in metal oxides could form the basis for next-generation non-volatile memory. It has been argued that the current in the high-conductivity state of several technologically relevant oxide materials flows through localized filaments, but these filaments have been characterized only indirectly, limiting our understanding of the switching mechanism. Here, we use high-resolution transmission electron microscopy to probe directly the nanofilaments in a Pt/TiO2/Pt system during resistive switching. In situ current-voltage and low-temperature (similar to 130 K) conductivity measurements confirm that switching occurs by the formation and disruption of TinO2n-1 (or so-called Magneli phase) filaments. Knowledge of the composition, structure and dimensions of these filaments will provide a foundation for unravelling the full mechanism of resistance switching in oxide thin films, and help guide research into the stability and scalability of such films for applications.