certain, probable or possible

The modal verbs are can, could, may, might, shall, should, will and would.

The modals are used to show that we believe something is certain, probable or possible:

Possibility:

We use the modals could, might and may to show that something is possible in the future, but not certain:

They might come later. (= Perhaps/Maybe they will come later.)
They may come by car. (= Perhaps/Maybe they will come by car.)
If we don’t hurry we could be late. (= Perhaps/Maybe we will be late)

We use could have, might have and may have to show that something was possible now or at some time in the past:

It’s ten o’clock. They might have arrived now.
They could have arrived hours ago.

We use the modal can to make general statements about what is possible:

It can be very cold in winter. (= It is sometimes very cold in winter)
You can easily lose your way in the dark. (= People often lose their way in the dark)

We use the modal could as the past tense of can:

It could be very cold in winter. (= Sometimes it was very cold in winter.)
You could lose your way in the dark. (= People often lost their way in the dark)

Impossibility:

We use the negative can’t or cannot to show that something is impossible:

That can’t be true.
You cannot be serious.

We use couldn’t/could not to talk about the past:

We knew it could not be true.
He was obviously joking. He could not be serious.

Probability:

We use the modal must to show we are sure something to be true and we have reasons for our belief:

It’s getting dark. It must be quite late.
You haven’t eaten all day. You must be hungry.

We use must have for the past:

They hadn’t eaten all day. They must have been hungry.
You look happy. You must have heard the good news.

We use the modal should to suggest that something is true or will be true in the future, and to show you have reasons for your suggestion:

Ask Miranda. She should know.
It's nearly six o'clock. They should arrive soon.

We use should have to talk about the past:

It's nearly eleven o'clock. They should have arrived by now.