Fellowships provide financial assistance for research and for costs of living while in graduate school. Some universities will not guarantee funding to graduate students for their work, and you'll need to find outside sources of income and support. Additionally, when applying for postdoctoral and faculty positions later, hiring committees will look very positively at applicants who have won these competitive awards.
You can apply for most research fellowships during your senior year around the time you apply to graduate school. We have compiled a list of various research fellowships students in physics and related fields can use while in graduate school. Please go to the specific webpages for each award to find more information, application requirements, and deadlines: