Equipment transport bag assemblies (20, 92, 98, 145, 152, 182) each including an upright, open-top, equipment-receiving bag (22, 110, 158) with associated equipment-handling assemblies (24, 92, 102, 164, 184). The assemblies (24, 92, 102, 164, 184) have load-bearing strap units (34, 114, 166, 186) operably associated with the transport bags (22, 110, 158) so that the strap units (34, 114, 166, 186) bear the primary loads during lifting and handling of the bag assemblies (20, 92, 98, 145, 152, 182).