I cut my scraps up into squares of sizes I use starting with 5" squares if I can get that size, and then into whatever sizes I can get with 1-1/2" being the smallest I will cut. Then I have plastic shoe boxes I put them into. I have written on the boxes with marker the size of squares in it.
If a scrap does have a full width of fabric I can cut a strip from, I will cut that first before cutting the scrap into squares.
And if the scrap is something I don't think I will be wanting to use any more of, I put it on our guild's put and take table.