I can mostly speak to how the USN used the few Zeppelins they bought.
But in WW1 the Germany Navy used their Zeppelins for a variety of purposes, mostly though it was for scouting for the High Seas Fleet, weather forecasting for operations, and yes bombing England several times as AAA and early planes simply couldnt reach their altitude.
Now fast forward to the early 20's and the US has realized the usefulness in having airships with long range and endurance to patrol her long coasts and to help the fleet with spotting.
So in total 4 different airships were operated by the USN, the AKRON, MACON, SHENANDOAH, and LOS ANGELES. They were primarily for spotting and patrol purposes, but also included ideas to be used as flying aircraft carriers, carrying small parasite fighters which would fly up, be caught on a hook, and then brought up into a small hanger in the ships.
Like so: https://en.wikipedia.org/wiki/File:F9C-2_Sparrowhawk_fighter.jpg
https://en.wikipedia.org/wiki/File:N2Y-1_USS_Macon_hangar_NAN9-75.jpg
The ships primary home was NAS Lakehurst in southern New Jersey (as it was also the primary arrival point of Zeppelin trips) and the ships even made use of the massive hanger that was also used by the Hindenburg and still stands today in use by the Navy.
https://en.wikipedia.org/wiki/USS_Shenandoah_%28ZR-1%29#/media/File:USS_Shenandoah_Bau.jpg
The experiment however was not in the end successful, 3 of the 4 crashed due to storms with large loss of life in 2 of them and the Navy quickly moved towards more versatile advanced patrol planes like the PBY Catalina as WW2 approached.
Non rigid blimps though would continue to be used in primarily a patrol and anti submarine role through WW2 to free up additional aircraft for needed roles.
The airships operations during the annual Fleet Problems was also unspectacular to justify the high budget costs, as the growing number of carriers in USN service and the growing development of their airwings meant longer scouting ranges though the fleet did attempt to make use of them, including fitting an oilier as a mobile tender.
https://upload.wikimedia.org/wikipedia/commons/7/75/ZR3_USS_Los_Angeles_an_Kriegsschiff.jpg
