Modal verbs are used to:
talk about obligations and necessity:
You must wash the dishes after the dinner.
I have to to go right now.
I had to walk four miles to get to the shop.
talk permission and prohibition:
You can go in now.
We must not stop the project.
They can't tell me where to go until Nick allows them.
talk about lack of obligation:
We did not have to buy apples.
You need not worry, everything will be all right.
You do not need to write a letter, we have written it already.
talk about abilities:
My son can run too fast.
He can't speak Spanish.
He can swim like a fish.
make a guess and to speculate:
They might be Ukrainian.
Where could I write this letter?
She could be in the kitchen.
make spontaneous predictions:
They will not play.
They may pass an exam if they learn hard.
She will be late, as usual.
make spontaneous decisions:
I will write a report about it.
He will not play there.