A streamlined approach analyzes block-level backups of VM virtual disks and creates both coarse and fine indexes of backed up VM data files in the block-level backups. The indexes (collectively the “content index”) enable granular searching by filename, by file attributes (metadata), and/or by file contents, and further enable granular live browsing of backed up VM files. Thus, by using the illustrative data storage management system, ordinary block-level backups of virtual disks are “opened to view” through indexing. Any block-level copies can be indexed according to the illustrative embodiments, including file system block-level copies. The indexing occurs offline in an illustrative data storage management system, after VM virtual disks are backed up into block-level backup copies, and therefore the indexing does not cut into the source VM's performance. The disclosed approach is widely applicable to VMs executing in cloud computing environments and/or in non-cloud data centers. The illustrative content indexing is accomplished without restoring the VM data files being indexed to a staging location.