Here are some very brief notes about NSF fellowships. Also see Advice for applying for graduate science fellowships by my student Philip Guo.
Broader impact is a major factor in getting fellowships accepted now. This wasn't true in the past, but apparently most of the applications have solid research components so broader impact has become a differentiator.
Students should emphasize any leadership role they have had.
Students should make sure that all of their application materials are of equal quality. There is a temptation to focus on the research statement, but panel members question who actually wrote the research statement if the other parts are poorly written.
If you are applying during your first year of graduate school, do get at least one recommendation letters from faculty at your grad school. It won't be able to say much specific, but the absence of such a letter is likely to be taken as a black mark.
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