A facial expression reminiscent of one who is retarded. It often involves eyes turned in different directions and a stupid smile.
In reply to that idiotic comment, I posted a picture of a retarded facial expression with the caption "This is my derp face."
by Banky Edwards February 10, 2011
A relaxed facial expression which perpetually holds an expression which can often be described as cute, awkward, and somewhat silly.

The word "derpy" is often used to describe such people.
Eric and Joe: Hi, Matt! :D

*Matt smiles awkwardly and gently waves as he passes them*

Eric: Aww, Matt's always so derpy all the time! I love that guy.

Joe: It's kind of his thing. He has resting derp face.
by akuwardmoments April 11, 2018