You know the phenomenon. No matter how hard your try, eventually, the little plastic tip on the end of your shoelaces (the official term is "aglet") will get crunched up, and slowly, you find yourself with a set of frayed laces. You could do the classic trick of burning the ends with a match to seize the fibers, but that's a temporary solution, and eventually, you'll end up exactly where you started.
Shoelaces are, of course, replaceable, and if you simply need a white or black pair for sneakers, or perhaps the classic golden variagated laces often found in leather workboots, you can switch them out if you like. But, so many pairs of shoes rely on the complement and/or contrast of the laces as a design element, and so often, you can't find a replacement.
So, instead, let's figure out how to fix shoelaces so they stay compact, useable, and fray-free.