Modal verbs are helping verbs which give extra information about the verb that they accompany. There are ten very common modal verbs in English. Each modal verb can express different functions depending upon the context in which it is used.

Here are five common modal verbs and their related functions:

Can- ability, permission, possibility
Must – strong obligation, logical conclusion
Would – past habits, past predictions, tentativeness
Will – habits, predictions
Should – mild prediction, mild obligation

To refer to past events using modal verbs the following pattern is common:
Modal + Have + Past Participle

• I failed the exam.  I should have studied harder. (Mild obligation in the past)
• The lights are out.  They must have gone out. (Logical conclusion about a past event)
• They were too tired.  They would have won if they had had more energy. (Prediction about a past event)

There are some exceptions to this:
To express strong obligation in the past must changes to had to.
To express past ability can changes to could. 
When you wish to express that somebody did something in a specific situation you use be able to.
Will for habits changes to would.

• All civil servants in Hong Kong had to speak English prior to the handover.
• I could do 300 pushups when I was eighteen.
• The fire killed most of the disco-goers, but three were able to escape.
• I remember my grandmother would always take a nap after lunch.