Emily Gilmore is Lorelai's mother and therefore Rory's grandmother. Emily had a limited relationship with her daughter as an adult, until they began to bond again with Rory needing money to get into Chilton Prep.
Emily was raises with a strict social code, attended Smith College, and is extremely wealthy. As a result she is constantly disapproving of her daughter's choices.
Although she's happily married to Richard for most of the series, they have a separation during season five and end up back together.
Rory: Grandma, I can't believe you found the recipe for Beefaroni.
Emily: It wasn't easy. Antonia thought I'd gone insane.
Emily: No one needs a comment from you.
Emily: (about the man that Lorelai got pregnant with at 16) Your father would have gotten him a job with his insurance business, and you two would be living a lovely life right now.
Lorelai: Christopher didn't want to be in the insurance business, and I am living a lovely life right now.
Emily: Oh yeah, far away from us.
Lorelai: Oh, here we go again.
Emily: You took that girl and completely shut us out of your life!
Lorelai: You wanted to control me.
Emily: You were still a child!
Lorelai: No, I stopped being a child the minute the strip turned pink, okay? I had to figure out a way to live. I found a good job.
Emily: As a maid! With all your brains and talent!
Lorelai: I worked my way up. I run the place now!