Draw-to-x abilities are those that allow you to draw cards until you have a specified number of cards in your hand, regardless of how many cards you have to start with. These contrast with typical draw abilities like "+2 Cards" or "+3 Cards", which draw the same number of cards every time you play them. If you play a draw-to-x card when you have more than the targeted number of cards in hand already, you draw nothing.
Draw-to-x effects include Library (7 cards), Watchtower (6), Cursed Village (6), Blacksmith (6), Way of the Owl (6), and Jack of All Trades (5). Closely related to draw-to-x are abilities that cause you to discard your hand before drawing a set number of cards; like draw-to-x cards, the result is that you end up with the same number of cards in hand every time you use them. These include Scholar (7 cards), Hunting Lodge (5), Minion (4), and Way of the Mole (3).
The draw-to-x engine is a deck archetype that relies on reducing handsize and producing in your Action phase, and then playing a draw-to-x card to recover the handsize. Draw-to-x decks require non-drawing Action cards as payload (e.g, Bridge, Coven, Nomad Camp), along with draw-to-x cards, and probably villages to grant you enough terminal space to play all your payload and draw cards. Disappearing money cards—non-terminal payload Actions that don't draw—are especially useful in a draw-to-x deck, since they reduce the amount of terminal space you need to activate your engine. Draw-to-x also pairs well with cards that allow you to discard for a benefit, such as Hamlet, Oasis, and Artificer: discard to get the full benefit, and then redraw to a full hand.
Draw-to-x engines are typically less reliable than ordinary draw engines, as they require both the payload and the draw-to-x card (and sometimes a village) to be in the starting hand. Moreover they do not cope well with non-Action stop cards, even strong Treasures and Night cards, since they can't be played before your draw-to-x card and will remain in your hand reducing the number of cards you can draw.