All modal perfect auxiliary verbs refer to the past.
FORM: Modal + Have (Infinitive) + Past Participle
1. must have done = we are almost sure something happened in the past
- Jane wasn't feeling well yesterday. She must have caught a cold.
- Bill didn't answer the phone when I called him. He must have fallen asleep.
2. can't have done = we are almost sure something did not happen in the past
- She can't have forgotten to send you an invitation. I gave her your address.
- They can't have gone to bed late. They were very tired.
3. may / might / could have done = it is possible that something happened in the past but we aren't sure.
- Laura hasn't arrived yet. She may/might/could have missed the bus.
- I didn't see Paul at work. He may/might/could have been ill.
4. could have done = we had the ability to do something in the past but did not do it.
- You could have told us about the new project!
- She could have called me when she arrived but she forgot.
5. should have / ought to have done = (a) it was the right thing to do but we didn't do it. (b) we expected something to happen but it didn't.
- You should have told him the truth.
- They ought to have received the cheque by now.
6. would have done = we wanted to do something but we didn't do it in the end.
- They would have emailed you but the Internet was down yesterday.
- I would have bought that DVD but I didn't have enough money.
7. needn't have done = it wasn't necessary to do something but we did it.
- You needn't have gone to the supermarket. I've already done the shopping.
- The weather was warm and sunny. I needn't have taken an umbrella.
