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