Do dogs understand human feelings, expressions or what we say?

I think that dogs do understand us to a point. My dogs know when I am happy or sad and they show me because of the way that they approach me. If I am in a good mood then they run up to me for me to play with them, but if I am sad or upset they will slowly approach me and just curl up by me. If I give them a stern voice they know to go lay down but if my voice is calm and happy then they know to run around. I am sure that dogs understand us more than we understand them.