Gradient/Opacity Troubles

[Ronald]

Hopefully I can explain this well enough. I'd like to be able to have one end of a image or solid shape gradate into invisibility/zero opacity. The closest effect I can find in Illustrator is feathering which lightly gradates all edges into invisibility. I tried playing with gradient mesh and blend modes, but they didn't work.

image link

Above is an example in how the black rectangle, on top of the illustration, gradually becomes transparent as it reaches the right-hand side. I'd like to learn how to accomplish this with solid shapes and maybe even photographs or artwork - particularly in Illustrator but also Photoshop. I know the above example was accomplished in Photoshop.