Must, Should, Have To

"Must" and "should" are modal auxiliary verbs, while "have to" needs an auxiliary and can be used in different tenses (don't have to, will have to, have had to, did you have to).

Present Time

1. expressing probability: must or have to.
Should is used more rarely and is a lower probability.

positive
This must be my glass, it is the only one with lipstick on it.

He is not picking up, he must be working.

He must have my phone because I have his.


You have to be kidding me!

He has to be home by now, it only takes him 15 minutes and he left half an hour ago.


I have installed a new antivirus program, your computer should be protected now.
Patrick should know the answer, he knows a lot of things.



negative
① the negative of 'must / have to' is can’t:
He must be really thirsty --- He can’t be very thirsty., and not “He mustn’t be very thirsty”.
Other examples:
This can’t be my glass, it has lipstick on it.

He can’t be working, it’s after 9.
This can’t be my phone, mine is over there.


② shouldn't:
You shouldn't have any problems finding the apartment but if you do, call me.

It shouldn't be too long before my parents discover that I have taken it, so we better leave soon.
Now stay still, this shouldn't take long.


2. meaning 'it is required'

positive
All three verbs can be used but in different situations.
① should: advice (there is no obligation). Means 'it is a good idea to':
You should see a doctor for this fever.
I think we should invite her to the wedding.
Should I apply for this job?

② must and have to: obligations, laws, rules, orders

- There are many details one could mention but generally speaking must is considered the more formal version and is often preferred in written laws and rules. Orders are also given with must, but in speaking it can usually be replaced by have to:
You must have a visa to go to those countries.

When a police officer stops you, you must remain in your seat while they approach the car.


- Must is also used to express the personal opinion that something is absolutely necessary, for example for oneself:
I must finally sit down and write that paper, it is due next week.
We must stay together, we are stronger that way.

or between friends, when we strongly recommend:
You must visit us soon.

You must see that film, it is really good!


- Have to is normally used for external obligation, which could come from a superior, a parent, a law, etc.:
I have to get home, my parents will be worried.

Everyone is doing overtime so I have to work late if I want to keep my job.
 
- It is important to note that in this meaning must is restricted to the present tense, while have to is a lot more flexible and is used in all tenses, after modal verbs, etc. That is why, regardless of the differences in meaning in the present, in all other tenses we use the respective form of have to, and not must. For example:
You will have to help me with those boxes, they are really heavy.

I am not feeling well, I might have to see a doctor.

Of course he doesn't know how to open a bank account, he has never had to do it before.
 
- In the present (and only there) you can also use have got to with the same meaning:
I've got to go now, the trains trains run only until midnight.

We've got to take the kids to the zoo, they are really bored at home.


negative
① shouldn’t:
They really shouldn't play in that building, it's really old and it might be dangerous.
You shouldn't eat so much junk food.

② mustn’t, don’t have to: In English there is a big difference between
a) mustn't: it is a bad idea, it cannot be done or there will be negative consequences
and
b) don't have to: don’t need to, it is not necessary.
In the first case it is a negative obligation. And in the second - lack of obligation.
In the first case there are negative consequences, in the second - you have a choice and nothing bad will happen either way. For example:
a)
You mustn't forget your keys.
You mustn't let him talk to you like that.


b)
We don't have to hurry, we have time.

I don't have to wear a suit to work, it's pretty casual.

Past time

1. Meaning "most probably" we use must, in the form:

must + have + done

This is the co-called perfect infinitive, or in other words "have" (which does not change form and is always "have" and not "has" or "had") and the past participle pf the verb (the third form).
It means that something most probably happened:
It must have rained last night, the streets are all wet.
It must have been very noisy.
He must have arrived already.
You must have met our new boss.


- In the negative the rule for present tense applies – can’t:
It can’t have rained last night.

It can’t have been very noisy.

He can’t have arrived.

You can’t have met our new boss.


2. "must" for past obligation can have two meanings
a) I did not do it, but I know it was necessary. Then you use "should":
You should have come to the party, it was great!

You should have been working instead of chatting!


b) It was necessary to do, and that us why I did it. Here we use "had to":

 We had to work late, that is why I didn’t call.

She had to get up early to go to the dentist before work.