could have / might have + past participle indicates something that was possible in the past (but not certain).
他们They 可能might (完成)have 错过missed (冠词)the 火车train.
They may have missed the train.
(它)It 本可能could (完成)have 是been 更糟worse.
Things could have been worse.
Note: could have can also mean "could have done but didn't": I could have helped, but I didn't. (I could have helped, but I didn't.)
Common Errors
- ❌ ~~He must forgot.~~ → ✓ He must have forgotten. — Speculation about the past requires "modal + have + past participle"; there is no form like "must forgot".
- ❌ ~~I should have went.~~ / Mishearing as oral speech ~~should of gone~~ → ✓ I should have gone. — After have comes the past participle; connected speech sounds like "of," but it must be written as "have."
- ❌ ~~I could help you yesterday, but I was busy.~~ → ✓ I could have helped you yesterday… — "Could have done" expresses "could have but didn't"; could + base verb only expresses general ability in the past.
- ❌ ~~You should had called.~~ → ✓ You should have called. — After a modal verb always comes the base form "have," never "had."