Curves, Tapers, Geometry

Hi all,
I’m struggling with tapering. I want to extrude a shape along a curve, and have it change as it follows the curve. I want to make it shrink or grow along the curve.
Also, is there a way to make one shape morph into another along a curve?

you can use the curve modifier.

Great, could you give me a keyword? I’ve already been trying to figure this out for a while. I messed all around with Curves and read and re-read the info about curves on the Blender Manual site, but I can’t figure out how to do it. It says it can be done, but no further info.