My purchased songs show on my iPhone but not in my itunes library on my computer

I have purchased songs from iTunes and they don't show up in my itunes library but they however do on my itunes on my iPhone. I have the latest version of itunes so can someone please help me?? I've googled it and things but nothing is helping! Also, I'm not sure if this problem has anything to do with Itunes Match? If it does, is there another way I can do it without paying every month?