The multidisciplinary nature of response robotics has brought about a diversified research community with extended expertise. Motivated by the recent accelerated rate of publications in the field, this paper analyzes the research trends, statistics, and implications of the literature from bibliometric standpoints. The aim is to study the global progress of response robotics research and identify the contemporary trends. To that end, we investigated the collaboration mapping together with the citation network to formally recognize impactful and contributing authors, publications, sources, institutions, funding agencies, and countries. We found how natural and human-made disasters contributed to forming productive regional research communities, while there are communities that only view response robotics as an application of their research. Furthermore, through an extensive discussion on the bibliometric results, we elucidated the philosophy behind research priority shifts in response robotics and presented our deliberations on future research directions.