Delta flew the DC-8 from the beginning of the jet age until about 1975; Delta also had a large fleet of DC-8-61 aircraft, which were re-engined in the early 1980s and were in service with DL until the late 1980s I believe. The DC-8s flew all of DLs "important: routes at the time, with many seeing service on the busy ATL-DFW-California routes as well as heavily travelled routes out of ATL to the US east coast and to some Florida cities. The Super 61s were DL's original 200+ seat airliner and were used on the then busiest routes......when the L1011 came along, then followed by the 757/767, the DC-8-61s were used on some secondary routes. My last DC-8-61 flight was from BOS to FLL in 1983 I believe; the Super 61s were also seen on many flights from ATL to cities like SAV, CHS, etc where capicity was needed. The DC8 was replaced in the end by DL's 72S fleet (DL started acquiring 72S aircraft in the early 1970s, after the NE merger, much later than most other carriers) and the Super 61s were replaced by 757s.
DL operated DC9-10s and then DC-9-30s - these aircraft saw service on basically all DL routes from Dallas eastward, focusing of course on the ATL hub (this was pre-CVG hub and pre-Western merger times). The DC9-10s left early on, in the late 1970s or early 1980s, and the DC9-30s remained in the fleet, on the shorter routes out of ATL (many of which are now operated by regional jets), until the mid 1990s. The MD88 replaced the last of DC9s - what happened was MD88s replaced 73S aircraft and 73S aircraft replaced the last of the DC9s.
Also remember that DL operated the CV880, another first generation jet, until I think the late 1970s.