A storage organiser with bins set at an angle make it easy for a child to take out and put back toys into the bins without having to open or close lids. These are excellent options as they take up very little space and are vertical-based storage units as opposed to bulkier and large toy box benches.
While not strictly toy boxes or chests, there are also nets available that act as spider webs that parents can simply tack up in corners to hold lightweight stuffed animals. These nets never touch the ground and do not take up any floor space.
So, no matter what your needs are, you can find all different types of toy chests, boxes, and storage units that will meet your capacity needs, design preferences, and size requirements.