Emptiness is the key notion of the Madhyamika school of Mahayana Buddhism, one of the two main Mahayana schools. Often over-simplified by conflation with anatman (no-self), it goes deeper: not just things, but actions, relations, constituents of mind and matter — everything is empty of intrinsic existence. Emptiness is what allows the interpenetration of co-dependent origination. The great expositor of emptiness and the founder of Madhyamika philosophy was the second century Indian monk Nagarjuna.
A word about Madhyamika: Madhyamika literally means “the middle way.” In popular discourse, this phrase is often interpreted like the story of Goldilocks and the three bears — neither too much nor too little but just right. While Buddha did speak, for example, of practice being not too tight or too loose, etc., that’s not what “middle way” means. The middle way of the Mahayana is a technical philosophical position denying the truth of any sentence and its negation. For example, reality cannot be captured by “it is raining” and it cannot be captured by “it is not raining.” This notion of the middle way is deeply connected to sunyata.
Note that Madhyamika and the other main Mahayana school, Yogacara, are not mutually exclusive. The Zen tradition freely takes from both systems, depending on context.