Tsunamis are high-impact, long-duration disasters that in most cases allow for only minutes of warning before impact. Since the 2004 Boxing Day tsunami, there have been significant advancements in warning methodology, pre-disaster preparedness and basic understanding of related phenomena. Yet, the trail of destruction of the 2011 Japan tsunami, broadcast live to a stunned world audience, underscored the difficulties of implementing advances in applied hazard mitigation. We describe state of the art methodologies, standards for warnings and summarize recent advances in basic understanding, and identify cross-disciplinary challenges. The stage is set to bridge science, engineering and society to help build up coastal resilience and reduce losses.