Opacity Mask
If working in CMYK mode.... make certain the "black" in the gradient is actually the Registration
black (yes, Registration)
If working RGB ensure the black is R0G0B0 and not simply K100%.
The above colors are required for masking to work properly and actually hide 100% of all the colors. If you find your mask is not hiding everything as you expect, it may be because the "black" in the mask is not full color.
Ensure the gradient object is on top in the stacking order. It will be used as a mask.
Select the gradient rectangle and everything you want to fade.
On the Transparency Panel (Window > Transparency) click Make Mask
button.

You'll see this new Opacity mask take effect on the artwork. From here, you may need to adjust the clip
or invert
options depending upon the artwork construction.

Working with Opacity Masks in AI is similar to working with Layer Masks in Photoshop. If you want to edit the Mask, you need to click the mask thumbnail on the Transparency Panel. Conversely, if you wish to edit the artwork, you need to click the artwork thumbnail on the Transparency Panel.
These are the basics of creating an Opacity Mask. Opacity masks can be created from vector OR raster content in Illustrator. Unlike Clipping Masks, Opacity Masks are helpful when you desire a mask which contains soft transitions in transparency. However, they will also work with hard edge objects if needed.
(CC2017 Transparency panel screen shot, but functionality is the same in newer versions)