Prismatic crystals provide a theory of ``coefficients'' in integral p-adic Hodge theory. After explaining the definition, I will explain how this notion sheds new light on some classical objects in both number theory (such as Galois representations over p-adic fields) and algebraic geometry (such as the Deligne-Illusie theorem for de Rham cohomology). Speaker(s): Bhargav Bhatt (University of Michigan)