Can I map the contents of an email to a new row?

I see a bunch of ways to send emails, but I’m looking for the reverse.

Upon receiving an email, I want to add its contents to a new row. More specifically, I’m looking to parse text in the body of an email, and/or parse a CSV attachment to a new row — if possible. What’s the best way to do that? Parser by Zapier does this quite well. But I’m looking for a way to do it natively.

I know the Gmail pack is down right now. If you’ll indulge me, let’s just pretend for a moment that it’s back up.

All help is appreciated.

Also, it doesn’t have to be an email. It could be Dropbox.