Modal verbs are helping verbs that indicate various levels of certainty, possibility, or duty. There are three rules that make them different from regular verbs or other helping verbs.
‘Can’ tells what is possible.
‘Could’ tells what was possible in the past. (When I was young, I could run fast, but now I can’t.)
'Could' is also often used like ’might’ to express limited probability, and as a polite way of requesting help or permission. Examples:
We use ‘will’ (or ‘be going to’-- not a modal verb) to talk about the future. ‘Will’ can also express determination.
It is often shortened to -‘ll.“He’ll go tomorrow, but she won’t.” (Won't is the negative contraction-- will+ not.) When ordering at a restaurant: “I’ll have the roast beef with mashed potatoes, please.” (You could also say, “I’d like the roast beef,” or “Could I have the toast beef, please?”)
See Practice the Future Tense for more on will and won't.
We use ‘would’ (or its contraction: -‘d) as shown above, for making polite requests:
-- Sue: “Would you like some more fish?”
-- Mary: “Thanks, but I’d rather have some ice cream now.”
(I’d is the contracted form of ‘I would.’ We also use you’d, he’d, she’d, it’d, we’d, and they’d:
-- “You’d like my brother if you could meet him. I think he’d like you, too. Maybe you can come home with me this summer. It’d be great for you to meet my family, and I’m sure they’d be thrilled to have you. We’d have a fantastic time!”)
We also use ‘would’ when our action depends on certain conditions. There are several conditional forms. You can say, “I will go if it doesn’t rain,” or “I would go, but I think it’s going to rain” (which means that in fact you won’t go).
You could also say, “If I won a million dollars, I ‘d travel around the world” (an imaginary or ‘unreal conditional’. You probably won’t win the money, so you won’t travel. Note that the verb after ‘if’ here is in the past tense form, even though you’re talking about the future.That’s the correct form for the unreal conditional tense. It makes it clear that this is a very unlikely event.)
You can also use ‘would’ with a conditional (if) clause in the past perfect to talk about how things might be different now if the past had been different.
There is a discussion of different conditional tenses, with more examples in English Verb Tenses.
We use ‘should’ and ‘ought to’ to give advice or to express duty.
‘Must’ indicates an action that is not optional: you have to do it. We use it for laws and inescapable duties or facts of life:
‘Must not’ expresses the same urgent obligation.
‘Must not’ is very different from ‘don’t have to,’ which means that an action is not required (but is permitted.)
There is more on 'should,' 'ought to.' 'must,' and other modals on Practice Giving Advice.
‘May’ is the correct modal to ask for permission (though ’could’ is also polite and ‘can’ is used quite often, especially by children.) ‘May’ also expresses limited probability.
‘Might’ suggests that something is unlikely, but possible. “It may rain tomorrow” means maybe it will rain-- I don’t really know. “It might rain” can mean the same thing, but suggests it is more likely that it won’t rain.
There is one more rarely-used modal verb: shall and shall not or shan’t.
In the past, shall was used for the first person future instead of will-- or they might be reversed to express very strong determination: (“You shall not die!” he cried. “I will not let it happen!”)
Shall is not used very commonly anymore except as an invitation or suggestion: “Shall we dance?” (Even then, “let’s dance” is more common, at least in the U.S.)