Modals to express permission / prohibition: CAN, COULD, MAY, MIGHT, BE ALLOWED TO, MUSTN'T, BE TO

Present and future

Can and may are used to give permission. May is more formal and less common in everyday contexts:

You can borrow my car if you want.
Children may use the pool with adult supervision.

The negative forms cannot/can't, mustn't and may not (more formal) are used to express prohibitions:

I'm sorry, but you can't stay here.
You mustn't touch that Ming vase.
Non-committee members may not vote on committee issues.

Used in the negative, be to can also express prohibitions:

You are not to do that again!

Can, could and may are used to ask for permission. Can is the most direct of the three, could is more formal and tentative, and may is the most formal:

Can I use your phone?
Could I have a glass of water?
May I start my presentation?

Might, which has a more tentative meaning, is very formal and is rarely used: 

Might I ask you a question?

When we talk about permission but we are not actually giving, refusing or asking for it, we can use can/can't or be allowed to:

Students can choose any topic for their project.
We can't eat in the library.
Are we allowed to smoke in this restaurant?
Will journalists be allowed to ask questions?

Past

Could can be used to express general permission in the past:

When I was a child, I could do basically anything that I wanted to do.

But when we talk about a particular action which was permitted and performed, we use was/were allowed to:

Although I was underage, I was allowed to enter the race.