What is Australia’s relationship like with its neighboring countries?

I know, generally speaking, a lot of Aussies (and probably Kiwis) identify more with the U.S. and the U.K. for obvious reasons. I also know Australia has partnerships with both countries. But, I wonder how well they get along with the Asian and Polynesian countries around them. Particularly the big ones like China, the Koreas, and Japan. Do they have trade deals with each other?