You'll need to earn CAPS to do the following:
- Build and upgrade rooms
- Build elevators to reach the lower floors
- Destroy Rocks blocking the construction of additional rooms in the lower floors
- Revive dead dwellers
You can earn CAPS by doing the following:
- Rushing Rooms
- Exploring the wasteland
- Completing objectives
- Leveling up Dwellers
- Increasing the SPECIAL Stats of dwellers
- Getting them from Lunchboxes
- Earned from Daily Vault Ratings
Additionally, dwellers with high luck has the probability of earning extra caps when collecting the resources from the room they're working in. Placing several lucky dwellers in the same room increases this probability as well.