There must be a hundred different structures you can build to house your compost pile. You can get from very simple like a pile with no structure all the way to a three bin rotation system or a large barrel mixer. Some people go for the expensive fancy systems because they are nicer to look at or because they don't want to get too dirty. Others don't care what they look like and even like to play in the dirt, so they go for the simpler no structure or simple structure type of a pile. Sometimes, you need something more complicated if you have a lot that needs to be composted. Currently, I have 2 composter types at my house. A pile of leaves that sometimes has a wire cage around it and a garbage can with holes drilled into it for kitchen scraps. Very simple, easy to build and easy to manage.
I like the pile because as I work I can just throw everything right there into the pile with no effort, rhyme or reason. I do have to go back and mix it up as it composts, but not too much. The wire cage helps to contain the pile somewhat so that it doesn't go everywhere or blow away. It goes up when there starts to be too many leaves to keep in place in the fall. When the cage is in my way, I just open it way up or take it down. This usually means that I am mixing the pile or it's time to throw it on the garden. Just about every time I have taken the cage down, it goes up in a totally new spot. That is just one more reason why I like it being so simple. I can change my mind as to where the best spot for it is whenever I need to.