This paper describes the first use of vacuum‐deposited YF₃ films as active materials in memristors. These YF₃ memristors function with extraordinary dual digital/analog operation modes. In both modes, the memorization states are all non‐volatile, with long retention times (up to 10⁶ s). In the analog mode, the memristors achieve a stable series of consecutive cycles of 64‐level potentiation and depression, with large ON/OFF resistance ratios (up to 7.2), and extraordinarily balanced linearity. With these YF₃ memristors, an excellent recognition accuracy of 97% in the classification of handwritten digits is achieved. Time‐of‐flight secondary ion mass spectroscopy, X‐ray photoelectron spectroscopy, and valance change memory modeling to examine the switching mechanism of YF₃ are used, discovering that fluorine vacancy species are responsible for the memristor behavior. Excellent high‐temperature stability during both operation and state preservation suggests that these YF₃ memristors might find applicability in neuromorphic computing under relatively harsh conditions.