The Old Magic is one of the magical systems in effect on Roshar.
Little is known about the Old Magic. It is mentioned only in passing in The Way of Kings as Dalinar explains how he gained something but lost all memories of his wife by striking a deal with a powerful spren known as the Nightwatcher. In one of the Interludes in tWoK, Baxil speaks about the boon and curse of the Old Magic, as well as the residency of the Nightwatcher in the Valley. Av says "It's not a game, no matter how the stories try to put it. The Nightwatcher doesn't trick you or twist your words. You ask a boon. She gives what she feels you deserve, then gives you a curse to go along with it. Sometimes related, sometimes not."
In Words of Radiance, it is indicated that Taravangian, king of Kharbranth, asked a boon of the Nightwatcher: 'The capacity to save this world from destruction.' It claims he was given that capacity and, with it, created the Diagram. The Diagram is a combination augury and plan written in a language created by Taravangian himself for the purpose which laid out how he could save Roshar. The curse that came with his boon is indicated to be that he is not always in possession of such capacity, and that his compassion for the results of the decisions he makes varies conversely with his level of logical reasoning. Some days he is as dull-minded as a Parshman and brought easily to tears as he realizes decisions he makes may bring death to innocents, while on others he is more intelligent and able-minded than the greatest scholar but regards everything he is ordering done with cold logic and an eye for the bigger picture of Roshar. As yet, he has had only one day of perfect mental capacity and he constantly wishes for just one more chance with such capability. (Citation needed)
In Oathbringer, it is revealed that the Nightwatcher is to the Shard Cultivation as the Stormfather is to Honor. We also learn that there is no record of anyone ever having had their curse lifted. Though this clashes with Dalinar's experience, as his memories of his wife, which had been stripped from him by the Old Magic's curse, begin slowly returning for unknown reasons.