Weberviruses are bacteriophages (phages) that can infect and lyse clinically relevant, multidrug-resistant (MDR) strains of Klebsiella. They are an attractive therapeutic option to tackle Klebsiella infections due to their high burst sizes, long shelf life, and associated depolymerases. In this study, we isolated and characterized seven new lytic phages and compared their genomes with those of their closest relatives. Gene-sharing network, ViPTree proteome, and terL gene-sequence-based analyses incorporating all publicly available webervirus genomes [n = 258 from isolates, n = 65 from metagenome-assembled genome (MAG) datasets] confirmed the seven phages as members of the genus Webervirus and identified a novel genus (Defiantjazzvirus) within the family Drexlerviridae. Using our curated database of 265 isolated phage genomes and 65 MAGs (n = 330 total), we found that weberviruses are distributed globally and primarily associated with samples originating from the gut: sewage (154/330, 47%), wastewater (83/330, 25%), and human faeces (66/330, 20%). We identified three distinct clusters of potential depolymerases encoded within the 330 genomes. Due to their global distribution, frequency of isolation and lytic activity against the MDR clinical Klebsiella strains used in this study, we conclude that weberviruses and their depolymerases show promise for development as therapeutic agents against Klebsiella spp.