My big mat lies flat the the cutting table. My smaller mat fits perfectly on a drawer "shelf" in my sewing cabinet and my itty bitty trimming mat is in a drawer in my cabinet.
My rulers are in a letter holder type unit on my cutting table.
I do have a mega giant size mat standing behind my china cabinet in the dining room but have not used it in a couple years. If I decide someday to open my cutting table all the way up, it will fit on there.