Deutsch Perfekt: Einfach Deutsch lernen is an excellent magazine for people learning German or if you are teaching yourself German. I first saw it in a bookstore in Berlin in the language section.

The articles are graded by difficulty. Any odd words have explanations (in German) at the bottom or side of the page. There is a glossary of some of the words and their equivalent translation in English, Spanish, French, Italian, Turkish, Polish, and Russian.

No Pulitzers are going to be handed out for the article content, but they are good. There is also a grammar section in the center of each issue with exercises.

If you live in Europe, a subscription is fairly affordable. But if you live in the U.S., it gets pretty steep. BUT: they have a PDF version that is much more affordable. Here is the subscription form (here it is in English in case you haven’t learned enough German for the first one).