If we are fairly certain about something, must, can't and couldn't can be use to express this.
For present situations the model verbs must, can't and couldn't are followed by the infinitive without to.
I haven't slept for two days. You must be exhausted!
The continuous infinitive can also be used.
Why is he wearing his uniform? He couldn't be going to school. It's saturday today.
For past situations we use the same modal verbs + have + past participle.
I can't find my book. I must have left it at school.
This composition isn't very good. You can't have spent very long on it.
NB: mustn't is not normally used when speculating about present or past situations.
If we are not certain about something but think it is possible, we use may (not), might (not) or could.
For present situations these modal verbs are followed by the infinitive without to. The continuous infinitive is also possible.
Moe's not answering my emails. He might be on holiday.
The continuous infinitive can also be used.For past situations we use the same modal verbs + have + past participle (the continuous form is possible).
I think we may have taken the wrong road. This doesn't look familiar.
NB It is not possible to use can when speculating about present or past situations.