How did Glorfindel appear in Fellowship after his fate in The Silmarillion?

I recently went through The Silmarillion a few months back, now going through LOTR, and this confused me. As I understood it, Glorfindel died while fighting one of Morgoth's Balrogs, and there was no mention in Fellowship of how Glorfindel returned (that I can remember). Was there another elf named Glorfindel, or was he revived by the Valar? Am I misremembering details in The Silmarillion?