On the evening of 15 January 2022, the Hunga Tonga-Hunga Ha’apai volcano1 unleashed a violent underwater eruption, blanketing the surrounding land masses in ash and debris2, 3. The eruption generated tsunamis observed around the world. An event of this type last occurred in 1883 during the eruption of Krakatau4, and thus we have the first observations of a tsunami from a large emergent volcanic eruption captured with modern instrumentation. Here we show the explosive eruption generated waves through multiple mechanisms, including: 1) air-sea coupling with the initial and powerful shockwave radiating out from the explosion in the immediate vicinity of the eruption, 2) the collapse of the water-cavity created by the underwater explosion, and 3) air-sea coupling with the air-pressure pulse that circled the earth multiple times, leading to a global tsunami. In the near-field, the tsunami impacts are strongly controlled by the water-cavity source, while the far-field tsunami, which was unusually persistent, can be largely described by the air-pressure pulse mechanism. Catastrophic damage in some harbors in the far-field was averted by just tens of centimeters, implying that a modest sea level rise combined with a future, similar event would lead to a step-function increase in impacts on infrastructure. Piecing together the complexity of this event has broad implications to the hazard in similar geophysical settings, suggesting a currently neglected source of global tsunamis.