Should I Apply to Fellowships?

[pchem2018]

I'm applying for the 2018 school year to several top tier schools, and all of the programs I am applying to will fully fund my PhD. However, many schools list possible fellowships that I could apply to as well (NSF, Hertz). Should I bother going through the application process for these fellowships as well, or should I just focus on my graduate school application if I'm already going to be fully funded? Are there any benefits to having a fellowship? Thanks!

[TakeruK]

Yes, you should definitely apply to fellowships. Most schools that fully fund their students also require students to at least apply to these fellowships in order to be eligible for internal funding.

The main advantages to applying are the prestige attached to the fellowship, potentially more freedom to choose the lab to work in or do the research that you want since a prof doesn't have to pay you out of their grant (or pay as much for you), and potentially saving your advisor money that they could spend on other things. Some fellowships also come with research funds that allow you to go to an extra conference.