MIGHT/MAY + HAVE + past participle (3d column irreg. verbs)

> when you are not 100% sure whether something happened or not in the past. You are guessing about what you think happened.

She may have stolen my lipstick.

This plane ditched on the river! It might have run out of fuel.

MUST + HAVE + past participle

> when you have a stronger opinion about what happened. You feel sure that something happened or that you can deduce it from the situation

He must have left the lights on because our electricity bill was huge.

She must have been beautiful when she was young.