Can pets read human emotions?

I wish that my dog was capable of that, but he's not, sadly. He's been in an abusive home before he got thrown away on the train station where we found him. It took us about 3 weeks to be able to capture him in order to take him to vet (even though he was starving and slowly dying from babesiosis). It took him three years to not be terrified whenever someone laughed, or made a sudden move, or a broom fell to the floor and the like. He's still a very shy and calm dog. He was clearly beaten.
Altough I know that he loves us dearly, he doesn't understand what it means if someone is crying. He never got the chance to develop emotion-reading skills.
I know that many dogs - and animals in general - are great at reading human emotions.