My husband built an open pull-out drawer and attached it to beneath the counter in my laundry. It will hold the large boards and can accommodate at least 4 or 5 or perhaps even more....and they are always out of the way and laying perfectly flat. Of course, there is always one on the cutting table.

Buy a skirt hanger and the clips on it will hold them and then they can go into a cupboard or on a hook (keep out of the sun) when not in use LOL

I store mine on a hook that I have on the wall but I use Pants hanger that have rubber between the wood so it gives a better grip. this keeps the holes From stretching and also keeps it from warping.

The cutting mat I warped in the car was a result of leaving it parked so the sun was shining through the rear window and it molded to fit the back seat ... I learned that the sun rays are the damaging factor. I cut that board in half and used skirt hangers to keep track of both half. ( I find that if I have to I can cut on any form of cutting board, but I would rather have them flat!)
When I paid fifty dollars for my next big cutting mat, I discovered the pants hangers ... no little gripper teeth to nick the finish ...
The top of a chest freezer is an excellent cutting table (not so great to store a mat on, but if push came to shove .... duct tape and a vow to never move the mat ... might provide a space) ... keep the mat as close to a corner - - away from the center - - to provide enough support that you don't warp the freezer door.
I really don't have a lot to add to the conversation, except! The sun rays warp the plastic ... I don't know why, but I know that is how it happens, and the way that it will warp is not determined by anything - - have never found anyone who has successfully gotten them to lay back down and straighten out.
As far as what to do with five cutting mats?
On my peg board, from my local hardware store, I found pegs that were almost six inches long from the wall ... with the pants hangers and strategically placed pegs, just hang them one in front of the other. I do it with my rulers, and yes, sometimes, I want the one in the back ... but the issue is storage ... not the immediate gratification of being able to touch each ruler once to get it ... so that is what I do with everything ... sometimes, I just have to hang things in front of each other.

oh, DUH! moment for me! I didn't understand your point!
Here is what I do with five cutting mats. <g> you weren't talking storage, were you? LOL
I have the warped one, and cut it into two pieces, so they are hung strategically around the bunkhouse, depending on where they fit ... I inherited a set of drawers, designed by a hubby for his quilty wife, and so when I bought the new cutting mat, I could afford more and bigger, and that is what I bought ... and, put the set of drawers in the big house with the big cutting mat on top .. this is where I do the big cutting jobs and squaring up a quilt top, since the cutting table is in the same place as the frame ... then, my daughter had a cutting mat that she didn't need any more, so I brought it out to the bunkhouse for those three am mornings I sometimes enjoy, so it is out here for those moments. And, the last cutting mat I have was purchased at a quilting class when I hadn't planned on cutting anything (long story about a not very well presented class instruction, but that is beside the point!) I needed it so I bought a small one from the quilt shop.
And, THAT! that is why I have, and what I do with more than one cutting mat. :D My mom says I always was a rather clever child, though not necessarily a pleasing one. LOL

I clip the hangers I get for my slacks to the tops of the med & small cutting mats I'm not using and store them in the closet. I've also labeled them with one of the millions of return address labels you get in the mail every day. So when I take one to class or retreat it's easy to retrieve.
The larger ones are either on the cutting table or on the floor for the huge mats.
This is my first response but I have enjoyed and learned so much from reading many of your responses to the questions posted for some time now. As a full time administrator and part time quilter, it's made my life easier.

Firstly, I have one large one in good condition..one large one that was left in the car.thus, has a few bumps and curves on it..but kept for a second (just in case )...and then there are the two 24" ones (one with measuring lines and 1 blank) and I have one that is irreplaceable which is 17"x6".....goes everywhere with me.

My large ones are stored under a bed in the guest room when not in use except for one that I keep on my cutting table at all times. My small ones I actually use a wooden pants hanger and hang them in the closet in my sewing room. I do that with my blocks for quilts also, that way the project is always in the same place when I need it and sometimes I just put the pattern in the hanger with the blocks if I think I won't get to it right away. I have not used the plastic clip pants hangers for the mats but have used them for the quilt blocks. I am afraid that the plastic clip ones might leave 2 marks on them or tweak them someway.

When in use, they just lay on my dining room table. It's only my husband and I, so we eat sitting in a chair. When not in use I put them under my bed with a towel over the top to collect the dust bunnies

Brenda

Well,under the bed is all taken up,so one is on my sewing table --that is until I need to turn my sewing room into a guess room,then the sewing table becomes a dressing table,complete with a fold out three angle mirror! The other cutting boards reside under the living room settee.My friends- who have much bigger houses, think it's hilarious that I have so many hidy holes for all my quilting stuff.I must say though that our weekly meetings are always in my home, they think my coffee is better !!
My lovely husband is very understanding though and they also all think he's great. Love to all, Letty.