How does drop system work in Dota 2?

Valve has recently launched a virtual store in Dota 2 where you can buy various items for your hero. But I heard that is possible to "drop" this items also for free, in game.

How does this system works? Is it completely random? Is it possible to drop all items available in the store?

Solution 1:

Every time you reach a new level you are guaranteed to get an item. There is also a random chance to receive an item after every matchmaking game.

You cannot receive keys (to open treasure chests) through random drops, nor some exclusive items that can be found only by opening chests (unusual couriers, other mythical items, etc.).