You can make a pattern of the curve and clamp it in place and use a flush
cutting router bit with a bearing on the shank end. Once the pattern is
clamped to your work you run the router bit against the pattern to mill your
groove.
max

I am making a headboard. The top will be curved. There will be slats that
want to fit into a groove in the top piece. How would you go about cutting
the groove into that curved headboard?

TIA.

Dick Snyder