The German Information Center USA publishes a weekly newsletter, "The Week in Germany". According to the website, it provides a weekly round-up of German politics, business and culture every Friday. "TWIG" focuses on stories of value to American readers, from German-American business news to German heritage to the best innovations from German scientists. Although it says it is aimed at American readers, I find it quite interesting and relevant for non-American readers.
They also publish a weekly German-language newsletter, which is distributed every Monday. The website says: If you are a German living in America or an American who wants to keep up with Germany and practice your German, sign up for the “Deutschland-Nachrichten” to stay in touch. The content is somewhat different from the English version. I find it possibly even more interesting than the English version, and it is definitely not just relevant for Germans in America or American readers. The German website says: Unser Newsletter "Deutschland Nachrichten" bringt Ihnen jeden Montag Aktuelles zu deutscher Politik, Wirtschaft, Kultur und Sport. Bleiben Sie über das moderne Deutschland informiert und halten Sie Kontakt mit Ihrer alten "Heimat", which sums it up nicely.