``Plus"- an online-only British journal (similar to Math Horizons):
http://plus.maths.org/content/
From their home page: ``Plus provides articles and podcasts on any aspect of mathematics, covering topics as diverse as art, medicine, cosmology and sport, a news section, showing how recent news stories were often based on some underlying piece of maths that never made it to the newspapers, reviews of popular maths books, and puzzles for you to sharpen your wits. We have a regular interview with someone in a maths-related career, showing the wide range of uses maths gets put to in the real world."
The intended audience is not limited to math undergraduates; science undergrads would find something interesting there, too. Some articles can be accessible even to high-school students.
And for those who read Polish, there is ``Delta" (which I used to read regularly in the paper version as an undergrad):
The 01/2013 issue contains e.g. an article on William Thurston and geometrization conjecture (by Zdzislaw Pogoda).
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