catch up on something—do unfinished work; do things that one has not had time to do until now:
- Confined to his bed for a whole week, Smith passed the time catching up on his reading.
catch up with something—(also: catch up to something )
1. overtake a bus, etc. by walking fast:
- Jane caught up with the bus that had almost left her behind.
2. keep pace with smth.:
- The fate of Africa depends upon economic advance catching up with political advance.