We can use modal verbs in the past by combining them with have + past participle.

Must have

We use must have + past participle to indicate certainty that something happened when we cannot prove it.

• Alice always arrives early, but today she is late. Something must have happened to her.

Can’t have

We use can’t have + past participle to indicate certainty that something did not happen when we cannot prove it. It is the opposite of must have. Notice how similar it is the Portuguese meaning (E.g., Não pode ter sido difícil - It can’t have been difficult).

• It can’t have been difficult for you to communicate in Mexico. You speak Spanish fluently.

May have / might have / could have

We use may have, might have or could have to indicate a possibility that something happened, but we are not certain about it. Notice the similarity to Portuguese (E.g., pode ter esquecido - might have forgotten).

• Rob might have forgotten about our appointment again.
• They could have got lost, maybe that is why they aren’t here.
• My husband hasn’t replied to my messages. He may have been very busy.

Should have

We use should have + past participle to express a recommendation about a past situation. This structure is also very similar to its Portuguese equivalent (E.g., deveria ter comido - should have eaten).

• He should have listened to me and avoided drinking.