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Abstract The resistance state of filamentary memristors can be tuned by relocating only a few atoms at interatomic distances in the active region of a conducting filament. Thereby the technology holds promise not only in its ultimate downscaling potential and energy efficiency but also in unprecedented speed. Yet, the breakthrough in high‐frequency applications still requires the clarification of the dominant mechanisms and inherent limitations of ultra‐fast resistive switching. Here bipolar, multilevel resistive switchings are investigated in tantalum pentoxide based memristors with picosecond time resolution. Cyclic resistive switching operation due to 20 ps long voltage pulses of alternating polarity are experimentally demonstrated. The analysis of the real‐time response of the memristor reveals that the set switching can take place at the picosecond time‐scale where it is only compromised by the bandwidth limitations of the experimental setup. In contrast, the completion of the reset transitions significantly exceeds the duration of the ultra‐short voltage bias, demonstrating the dominant role of thermal diffusion and underlining the importance of dedicated thermal engineering for future high‐frequency memristor circuit applications.