Modal verbs + past participle

Should (Not) Have + Past Participle

We can use should have + past participle to criticize a past action, or to talk about something you regret in the past. 

• She should have lied when she said the truth. (She should have lied, but she didn't)
• I should have told her the truth from the beginning.
• She should have remembered my instructions. Now it's too late.
• They shouldn't have seen such a horrible movie.
• She shouldn't have done that!
• He shouldn't have forgotten her instructions.

Could Have + Past Participle
We can use could have + past participle to talk about unreal situations in the past. It usually suggests that the power or ability to do something was there, even though the path wasn't chosen.

• I could have been someone bigger. (I had the chance to do so, but I didn't)
• He could have gone to college, but he became a writer instead.
• I could have been rich, but I lost my chance.
• I could have asked her to be my girlfriend.
• I could have got married, but instead I decided to concentrate on my career.

May/Might (Not) Have + Past Participle
We can use may/might have + past participle to talk about uncertain events in the past and to make guesses about past actions.

• She might have lied about her previous job. (We suppose this, we are not completely sure!)
• Someone might have told her to call us.
• Who might have said that?
• She might have known something about the robbery. 
• They might not have seen last part of the movie.
• She might not have recognized me because my face was a bit swollen.
• The bathroom might not have cleaned when inspectors complained about it.

Also, to make deductions about what activities were in progress in the past, we can use the continuous form:

• When she told you that, she might have been lying.
• Someone might have been seeing the car when the accident happened.
• They might have been talking when they were interrupted.
• She might not have been concentrating when she made the mistake.
• She might not have been thinking when she took that decision.
• He might not have been listening when the teacher said his same.

Must Have + Past Participle

We can use must have + past participle to express conclusions about events in the past.

• She must have lied when she told you that. (We are almost sure that she lied)
• Someone must have been seeing the car when the accident happened.
• The sidewalks are wet, it must have rained overnight.
• It must have been love but it's over now. (Roxette song)
• He must have drunk all the milk, there is none left!
• He's not answering the phone. He must have gone out.

Also, we can use the continuous form:

• She must have been listening behind the door.
• Someone must have been seeing the car when the accident happened.
• He must have been doing something bad when the teacher saw him.
• She must not have been listening when the teacher said her name.

To express negative conclusions, suggesting that something is impossible we use the form: Can not have + past participle. (Warning, don't make this mistake > "She mustn't have been sick")

• She can't have lied when she told you that.
• The sidewalks are dried, it can't have rained overnight.
• He can't have drunk the milk, he wasn't here yesterday.
• She can't have been listening behind the door because she doesn't do those kind of things.
• He can't have been doing something wrong because he behaves very well.

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