Everything worth knowing, nothing that isn't.
HLR vs VLR vs HSS
The HLR is the permanent system of record for a subscriber's home network. The VLR is a temporary working copy held by whichever MSC currently serves the handset. The HSS (Home Subscriber Server) is the 4G Diameter-based successor to the HLR. See /answers/what-is-vlr, /answers/what-is-msc, and /answers/diameter-s6a-explained.
Why the HLR matters for deliverability
A live query against the HLR reveals whether a number is active, which operator currently owns it (crucial after number porting), and whether the subscriber is roaming. Exposed as a standalone API this is HLR Lookup — the single most useful list-quality check before an A2P send. See /products/hlr-lookup and /answers/what-is-hlr-lookup.