I saw 2 giant rats last night in my front yard.  I was making dinner and kept hearing something very quiet outside, hit the light and saw 2 possums.  Went outside and one jetted over the side of the hill, other just kept slowly walking toward me. 

Several years ago I kept hearing one under the sink at another place I used to live.  I noticed it had chewed out the bottom corner of my garbage bag and eaten some chocolate muffin, so I went to ace and got a rat trap and bated it with chocolate muffin.  At 3 am I get woke up by a loud SNAP! and went to find a 14" rat in my trap!  Just to be sure I took it outside, shot it with my .22 and threw it over the side of the hill.  That was the first rat I'd ever seen in person.