Speculating about past events

 'It must have been a UFO.'

Imagine that you go to your friend's house, but when you knock on her door there is no answer. You then notice that her car is not there, so the conclusion you come to is that she must have gone out.

Let's take a look at that last part again: she must have gone out (must + have + past participle)

This form is used when we are speculating about past events i.e. we don't know for sure what happened, but have an idea.
In the above sentence must is a modal auxiliary verb which shows we are pretty sure about what happened. If we are not so sure, we use 'She could have gone out' or 'She might have gone out'.

Let's look at some other examples:

'Paul looks tired, he must have been out late last night.'
'I could have won the race if I had trained harder.'
'He might have gotten really sick if he hadn't started taking care of his health.'
'She may have taken the day off, because I haven't seen her today.
'I saw a strange light in the sky last night. It could have been a UFO!'

State Verbs

• She looks sad. She must have ___ some bad news.
  
  having
  have
  had
  has
  
  
• It might have ___ raining.
  
  stops
  stopped
  stop
  stopping
  
  
• She must have already ___ my name.
  
  knows
  know
  knew
  known
  
  
• He may have ___ them in his car.
  
  taked
  taken
  takes
  took
  
  
• The bird is gone, it must have ___ away.
  
  flow
  few
  fly
  flown
  
  
• He must have ___ himself after falling off his bike.
  
  hurt
  hurts
  hurted
  hurting
  
  
• The sign is missing, they must have ___ it.
  
  remove
  removing
  removes
  removed