“Had to” vs. “must have”

The modal verb must has two past tense forms: had to and must have. Which form we use depends on whether we want to express obligation or if we want to say how certain we are about the probability of something happening. 

This table below shows us the past tense of must and have to and when to use them.

Must / have to
present past
When expressing obligation, we say:

I must go.
I have to go.
When expressing obligation, the past of must and have to is always had to:

I had to go.
They had to be there at 2 o'clock.
When expressing a personal opinion about probability (deduction), we use must to express that we feel something is true:

He must be here.
It must be great.
When expressing a personal opinion in the past, we use must have, NOT had to:

He must have been here.
He had to be here.
It must have been great.
It had to be great.