Everything worth knowing, nothing that isn't.
The MSC in the SMS-MT flow
Delivery is a two-step SS7 exchange: the SMSC sends SendRoutingInfoForSM to the HLR to find the serving MSC, then MT-ForwardSM to that MSC, which pages the handset, delivers the SM, and returns the outcome that becomes your DLR. See /answers/ss7-map-explained and /answers/what-is-dlr.
The MSC on 4G and 5G
In an all-IP 4G/5G network the MSC's role is taken by the MME (4G) and the AMF (5G). SMS is then delivered either via SGs fallback through a legacy MSC, or over IMS (SMS-over-IP). This is why SS7 and the MSC persist for SMS even as voice and data move fully packet-switched. See /answers/diameter-s6a-explained.