The meaning of 牛气 and 很牛 I have seen one of my language partners use 牛气 and 很牛, but he couldn't explain it to me. The context suggested it meant something like "bullshit" or "you are kidding me", a sign or disbelief, but the dictionaries I tried only suggested literal cattle-related translations. Do they have another meaning?
As a slang, 牛 could be used for expressing awesome.


  在中国口语中的“牛”，已经被引申为一个形容词，意思为“厉害、有本事”，例如“你太牛了！”（标准：你太厉害了！）。这个词通常为褒义词，通常用于赞扬、形容某人很厉害，很有本事，很有胆量。也通常用于口语中的调侃。


So 很牛 means very awesome. 牛气 means arrogant ; self-important and also awesome.