1. "sssssshheeeeessh" If you want them to leave, like a hissing sound.
2. A squeaking (by pursing lips together) to calls them or tell them you are interested to play.
Generally I don't believe cats really try so much to communicate - at least I don't get this impression.
I would say that with dogs they understand a lot more. They understand the concept of pointing and use it to communicate something of interest to me. For example, one of my dogs ran out of the gate and the other dog pointed to where they went using their entire body as an arrow. Another time a ball was lost in a stack of tires, so the dog requested help from me to retrieve it my pointing. I can ask "where is <object they know>" and they'll take me to it, or help me search for it - to the point where one of my dogs will help me look for my keys.
My dogs will also try to communicate with me too, mimicking what they believe I sound like. "Helllooooo" they really try to copy as a greeting. They also like to get involved in singing too - I think they somewhat enjoy some music.
What I like about my dogs too is that they understand the more subtle things. When two people are arguing or speaking heatedly they will try to break them up by pushing in-between. They are not allowed into certain rooms unless invited, but a small sideways nod lets them know they have a one time pass.
Dogs also very much like routine, the human world is confusing and if you delay feeding for a few hours for example, they don't understand why. They often do their best to fit in if you help them to.
I think people really underestimate how smart dogs can be. They * really * try to communicate back, but they are mostly unsuccessful. Try sometime to take an interest in their attempts to communicate with you, encourage it even. If they think they can communicate with you, you'll have a much better time. My dogs even help me keep my daily schedule.