This paper introduces a novel service for distributed detection and summarization of crowd-sensed events. The work is motivated by the proliferation of microblogging media, such as Twitter, that can be used to detect and describe events in the physical world, such as protests, disasters, or civil unrest. Since crowd-sensed data is likely to be distributed, we consider an architecture, where the data first accumulates across a plurality of edge servers (e.g. cloudlets or repositories) and is then summarized, rather than being shipped directly to its ultimate destination (e.g., in a remote cloud). The architecture allows graceful handling of overload and bandwidth limitations (e.g., in scenarios where capacity is impaired, as the case might be after a disaster). When bandwidth is scarce, our service, BigEye, only transfers very limited metadata from the distributed edge repositories to the central summarizer and yet supports highly accurate detection and concise summarization of key events of global interest. These summaries can then be sent to consumers (e.g., rescue personnel). Our emulations show that BigEye achieves the same precision and recall values in detecting key events as a system where all data is available centrally, while consuming only 1% of the bandwidth needed to transmit all raw data.