Tsunami deposits are the primary source of information on (past) large tsunami events and thereby are crucial for accurate hazard assessments. Tsunami deposits studies have developed over the last three decades, but this is still a young geoscience discipline. Following the 5th International Tsunami Field Symposium in 2017 an opportunity arose to publish a Special Issue focusing on present knowledge and future research challenges. This paper aims to briefly review current state‐of‐the‐art research, summarizing major findings and gathering relevant works that describe the progress achieved over the last three decades. In this paper the relevance of tsunami deposits, their peculiar sedimentary characteristics and their differentiation from other high energy events are presented. Especially over the last decade an incredibly high number of studies have been published on tsunami deposits, many of which are of a high quality and provide detailed literature reviews. Some of these studies represent the current progress discussed here. Challenges are also introduced, to spur a discussion on future scientific questions that can and should be addressed by tsunami geoscientists. Coupling onshore–offshore records is an area where tsunami geoscience faces some of its major challenges. Moreover, the application of non‐destructive high‐resolution techniques to study the internal structure and composition of tsunami deposits can also provide an opportunity to further examine deposits, and from this derive physical parameters of the forcing mechanism. Another topic is better understanding of the erosional signature of tsunami events and a continuation of the effort to better incorporate age‐estimation methods by developing more accurate dating methodology. Finally, there is also the need for the improvement of empirical, forward and regressive numerical models to better contribute to the characterization of tsunami events.