On Dec. 22, 2018, at approximately 20:55-57 local time, Anak Krakatau volcano, located in the Sunda Straits of Indonesia, experienced a major lateral collapse during a period of eruptive activity that began in June. The collapse discharged volcaniclastic material into the 250 m deep caldera southwest of the volcano, which generated a tsunami with runups of up to 13 m on the adjacent coasts of Sumatra and Java. The tsunami caused at least 437 fatalities, the greatest number from a volcanically-induced tsunami since the catastrophic explosive eruption of Krakatau in 1883 and the sector collapse of Ritter Island in 1888. For the first time in over 100 years, the 2018 Anak Krakatau event provides an opportunity to study a major volcanically-generated tsunami that caused widespread loss of life and significant damage. Here, we present numerical simulations of the tsunami, with state-of the-art numerical models, based on a combined landslide-source and bathymetric dataset. We constrain the geometry and magnitude of the landslide source through analyses of pre- and post-event satellite images and aerial photography, which demonstrate that the primary landslide scar bisected the Anak Krakatau volcano, cutting behind the central vent and removing 50% of its subaerial extent. Estimated submarine collapse geometries result in a primary landslide volume range of 0.22-0.30 km3, which is used to initialize a tsunami generation and propagation model with two different landslide rheologies (granular and fluid). Observations of a single tsunami, with no subsequent waves, are consistent with our interpretation of landslide failure in a rapid, single phase of movement rather than a more piecemeal process, generating a tsunami which reached nearby coastlines within ~30 minutes. Both modelled rheologies successfully reproduce observed tsunami characteristics from post-event field survey results, tide gauge records, and eyewitness reports, suggesting our estimated landslide volume range is appropriate. This event highlights the significant hazard posed by relatively small-scale lateral volcanic collapses, which can occur en-masse, without any precursory signals, and are an efficient and unpredictable tsunami source. Our successful simulations demonstrate that current numerical models can accurately forecast tsunami hazards from these events. In cases such as Anak Krakatau's, the absence of precursory warning signals together with the short travel time following tsunami initiation present a major challenge for mitigating tsunami coastal impact.