Help With Lawn Border

[ickysully]

Hello all, so I am trying to make my lawn look better than what it was and I am having trouble with where the edge of the lawn meets the driveway. My lawn is higher than the driveway and slopes down to the drive. The border between the two is rough with dead grass and run off soil from the lawn. I was wondering if anyone has any suggesstions on how to make an edging for this that looks good and prevents the dead grass and soil from leaking onto the driveway.

I have attached a couple of pictures.

Thank you!

Sully