PROFICIENCY ENGLISH: GRAMMAR. MODALS IN THE PAST.

Could and would are the only two modals we
commonly use on their own to refer to the past:

I could drive a tractor before 1 knew how to drive a car.
(= ability)

Modal Perfects
Other modals may refer to the past when used with
the Perfect (have + -ed).
We use moda1 Perfects in
three ways:
1.-to speculate about events, or imagine the opposite
had happened:
1 would have talked to him but 1 didn't have time.
You should have told me you were coming.
They ought to have informed us of the change.
We were lucky - the whole thing could have ended in
disaster.
You needn't have gone to so much trouble.
You might have warned me.
2.-to talk about past events when we are not sure
whether they happened or not:
1 can'tfind my diary anywhere - 1 suppose 1 could have
left it at home. (= it's possible) She may have
phoned my office after 1 left. (= it's possible)
She can't have lefi already! (= 1 don't think she has)
She must have given it to someone else. (= I'm almost
certain) They might have gone home by now. (= it's
possible) They should have got there by now. (= 1
think so)
3.-to talk about possibility in the present and future.
This is a form of the Future Perfect :
You should have already gone through immigration by
the time 1 get to the airport .
SOURCE: GRAMMAR AND VOCABULARY FOR CAMBRIDGE ADVANCED AND PROFICIENCY. LONGMAN. PEARSON EDUCATION LIMITED.