There are different ways to store a knife. The cheapest and unfortunately a common way to store knives is just throwing them into a drawer. It’s dangerous, especially when knives are sharp (unless the blade is covered by a sheath). Worse, the sharp edge of the knife can damage other things in the drawer, and other things the edge of the knife.
Slotted knife block
In the Western world, the most common way is storing knives in a slotted knife block, usually made of wood, most of the time sold as a set together with the knives. This is a good way of storing knives, but it has to be assured that the knives are clean and dry when inserting them in the block, so that the slots in the block stay clean.
Magnetic wall strip
Here, a magnetic strip (usually made of wood) is attached to the wall, with the magnets holding the knives in place. It’s a clean way of storing knives and puts your knives on display in the kitchen.
Magnetic knife block
It serves the same purpose as a wall strip, but without having to drill holes into the wall.
It’s one of the less common ways of storing knives, but has the advantage of keeping them out of sight. It’s a safe way of storing knives when having small children, especially in combination with locked drawers.
It’s an alternative to drawer docks, mounting a knife holder under the cabinet or behind a cabinet door. Storing knives in a holder behind a cabinet door is the common way of storing knives in Japanese kitchens.
Professional chefs usually carry their knives with them in a knife roll (bag), as the knives usually are their personal belonging and not owned by the restaurant.
Knife sheath or saya
Putting the blade of the knife in a sheath is not a common way to store knives in the kitchen, but for outdoor knives, which usually are put into leather sheath. Reasons why kitchen knives could be put into a sheath would be if a knife is stored in a drawer, carried around or put away in a box for a longer period of time.
A knife sheath makes more sense for valuable knives with a delicate edge, which is why they are more common in Japan. Japanese knife sheaths are usually made of wood and called “saya”.
A Saya needs to match with the blade shape. The blade is usually protected from slipping out by a pin, which holds the knife behind the choil.
For Western knives, there are plastic sheath available, which usually only cover a part of the blade, but for the full length of the edge. Thus they are more universal.