Get custom category of post

I’ve got a custom taxonomy for my ‘articles’ and custom categories within this that hold articles/posts. I want to be able to get the category name of the selected post from within that post loop. I’m able to get the title, content, author, comments etc but can’t work out how to get that category.

Is there anyway of doing this?

Also, on side note is there anyway to get an archive list for the custom categories for my side bar. (Like wp_get_archives())