I very seldom use bias binding, only on quilts with curved edges, so bias binding left-overs are not an issue for me. If you meant straight binding scraps, I learned very early on how to closely estimate what I needed to cut so that I don't have more than a couple inches left after binding any quilt. Those get tossed.

Wow! You all have great ideas...... and to think...... I thought I was going to have to find a bigger box. Yeah! Don't need to do that now!!

I put them on scrappy quilts or iron them open and use them as strips in a scrappy

I have always said I was going to use it in a scrappy binding, but that has yet to happen, so for me the answer would be that I put it in a bigger container. :-) (The funny thing is that I do a fair amount of scrap quilts and tend to use only fabric left from that particular quilt for binding.

I make scrappy binding and use on my scrappy quilts.

I cut my binding 2½" -- I can use mine as a strip piece like a jelly role. Or sometimes I just put a bunch of leftovers together for a scrappy binding.

scrappy bindings, small bindings, open for scrappy strips( I use 2.5" binding strips)...

They make great beginners and enders when sewing.
Most I iron open and make HST. I plan on making a HST quilt someday so use alot of scraps for them.

I roll up the pieces in individual rolls and store it in a basket where I can pull pieces to bind odd creations like mug rugs or pot holders, etc.

I also sew them together and use them on scrap quilts or fun quilts for the grandchildren.