A/V + 던 can be used in three main ways:
The thing I was doing that was interrupted (중단) — often preceded by 아까, 지난주, 지난밤, 지난달…:
아침에 마시던 커피가 차갑게 식었어요.
The coffee I was drinking (and did not finish) this morning has gone cold.
읽던 책을 도서관에 반납해야 했어요.
I had to return the book that I was reading (but did not finish) to the library.
뜻밖의 전화를 받고 통화를 끝낸 후에 하던 일을 끝냈어요.
After an unexpected phone call I finished the work I was doing (prior to the call).
하던 대화를 계속 했어요.
We continued the conversation we were having (before we were interrupted).
먹던 밥을 내일의 식사를 위해 냉장고에 넣었어요.
I put the food I was eating (but didn’t finish) in the fridge for tomorrow’s dinner.
지난주에 통근하면서 공부하던 책을 잃어버렸다고 생각해요.
Last week while I was on the way to work I lost the book I was reading (but didn’t finish).
자유 시간이 있어서 지난 달에 보던 시리즈를 계속 보려고 해요.
I have some free time, so I intend to read the book I started last month (but haven’t finished yet).
Reminiscing on a continued action in the past (회상) — typically used with 예전, 전에, 오래…:
사귀던 여자가 저의 회사에서 일하고 있어요!
The girl I used to date is working at our company!
다니던 초등하교가 철거될 예정이에요.
To attend elementary school is scheduled to be torn down.
오래되 친구들과 놀던 공원을 지나갔어요.
I passed the park where I used to play with my old friends.
그 차는 아버지가 예전에 타시던 차와 똑같아요.
That car is just like my father’s old car.
어릴 때에 먹던 과자를 이제는 못 사요.
You can’t buy the snacks I used to eat when I was young anymore.
학당에 근무하던 동료와 골프를 쳤어요.
I played golf with someone I used to work with at the academy.
2년전까지 일하던 회사가 요즘 폐업돼네요.
The company I used to work for two years ago is now closed.
귀엽던 아역 배우가 못생긴 남자로 변했어요.
The cute child actor has grown into an unattractive man.
예전에 수승대는 소풍 가던 곳이었어요.
I used to go on picnics in Suseungdae.
중동 음식 중에 제일 맛있던 게 뭐예요?
What was the most delicious food in the Middle East?
힘들던 군대생활이 생생하게 기억나요.
I remember the difficult time I had in the army vividly.
Recalling an action I did for some time, but has changed/stopped very recently — typically used with 자주:
입던 옷이 제 동생에게 주었어요.
I gave the clothes I often wore to my little brother.
시끄럽던 학생들이 갑자기 조용해졌다.
The noisy students suddenly fell silent.
자주 듣던 곡의 가사를 배웠어요.
I learned the lyrics to the song I often listened to.
그 자주 가던 맛집이 이제 경영진이 바뀌었다.
The restaurant we frequented is under new management.