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Modal verbs to talk about the past — reference

modal verb + (not)+ have + past participle

Verb	Meaning	Example
could have done	something was possible in the past or there was a probability, but it didn't happen	He could have slept till evening but the alarm clock woke him up.
should have done	it would have been a good idea to do that	You should have told me that the meeting was cancelled.
must have done	it was very likely	Where are my gloves? I must have left them in the car.
might have done	it was probable	They might have misunderstood us.
would have done	something was possible, but it didn't happen	I would have telephoned that company, but there wasn't a phone number on their website.