I have a 3.94 GPA (got one stupid B my freshman year). I am a junior now. I have been doing undergrad research since the start of my sophomore year. This past summer I did an REU that was 10 weeks of full time research. I know I am going to have great letters of recommendation. I am also planning on continuing to do undergrad research so by time I go to apply for grad schools I will have 4-5 semesters of research as well as two summers of research (I have something lined up if I can't get into another REU or land an internship for next summer). Let's just say that my performance continues and I continue to get As in my classes, and I do well on the GRE. What are my chances of getting into a top ranked school? I feel like I'm doing everything right. I couldn't be working harder or getting more research experience. But I also just have this feeling of dread that despite doing everything I can to get into the best grad school that I can, it still somehow will not be enough. I want to go to a big name school. Do I have a chance at Ivy League, or is the selection process somewhat arbitrary and I still will struggle to get in? I just have this feeling (based on no actual facts) that it's not going to be enough and I won't get into my school of choice despite achieving my maximum potential. So... do I have a shot? EDIT: I go to a second tier school right now.