What to do with wasted space in closet?

I use plastic crates for storing out-of-season items in the back, you can kinda see the contents, and they are light weight enough to pull out easily.

I would do anything for that much extra space. I would store extra linens, vases, out of season decor, out of season clothes, serving pieces rarely used, craft supplies, anything you do not need on a daily basis.

I would store Christmas decorations in that space. You would only pull them out once a year so they can be put in the back. You could do the same thing with decorations for Easter, Thanksgiving, Fourth of July, etc. Just mark your boxes for which holiday.

I had an extra large closet before. I put big stuff in it like the pack of toilet paper or paper towels, cases of water bottle and soda, etc. I love that closet, I wish I had one in my current home.

What could you do with it? You could trade it for MY linen closet--I'd give my right arm for that much closet space! All kidding aside, the first thought that came to mind was slide -out drawers. However, the other commenters here are spot on with suggesting storing out--of-season items in the back of each shelf.

Store out of season items in baskets and put labels on them.

I have sort of the same problem but maybe not. I hear you saying that the depth of the shelves is the problem, not what to store there? Or maybe I just think that because my linen closet has shelves that are too deep for me to reach in the back, but I know I want to store linens on all the shelves. The best solution I have found is to have shallow, long baskets. The problem is these baskets are hard to find. I always forget what sheets are in piles in the back.

To avoid this storage area becoming like Fibber McGee's closet, you need it set up for accessibility so you can quickly see, and get at what is in there, and an arragement scheme that involves the least amount of stacking items on top of one another.

If you are dependent on this closet as a main storage area in the home, then I would advise you to check into re-vamping it with sliding shelves. Pictures below show styles that are efficient use of space.

I have closets like this. It would help to know what you intend to store, but if it's only linens, then I would use slide out drawers on the lower shelves. Lowe's has plastic drawers that are easy to install or you can just use baskets that can be pulled out. Label each basket with the contents. If you want to store other items, like cleaning supplies, use large turntables. Bed, Bath, & beyond have these. You can use small plastic buckets to contain very small items on the turntables. Small plastic paint pails are inexpensive and come in many sizes. You can also use plastic drawer bins with 2-3 drawers to sit on the shelves.