Memristive systems present a low-power alternative to silicon-based elec-tronics for neuromorphic and in-memory computation. 2D materials have been increasingly explored for memristive applications due to their novel biomimetic functions, ultrathin geometry for ultimate scaling limits, and potential for fabricating large-area, flexible, and printed neuromorphic devices. While the switching mechanism in memristors based on single 2D nanosheets is similar to conventional oxide memristors, the switching mechanism in nanosheet composite films is complicated by the interplay of multiple physical processes and the inaccessibility of the active area in a two-terminal vertical geometry. Here, the authors report thermally activated mem-ristors fabricated from percolating networks of diverse solution-processed 2D semiconductors including MoS2, ReS2, WS2, and InSe. The mechanisms underlying threshold switching and negative differential resistance are eluci-dated by designing large-area lateral memristors that allow the direct observa-tion of filament and dendrite formation using in situ spatially resolved optical, chemical, and thermal analyses. The high switching ratios (up to 103) that are achieved at low fields (≈4 kV cm−1) are explained by thermally assisted electrical discharge that preferentially occurs at the sharp edges of 2D nanosheets. Overall, this work establishes percolating networks of solution-processed 2D semiconductors as a platform for neuromorphic architectures.