Gradual typing enables programming languages to seamlessly combine dynamic and static checking. Language researchers and designers have extended a wide variety of type systems to support gradual typing. These efforts consistently demonstrate that designing a satisfactory gradual counterpart to a static type system is challenging, and this challenge only increases with the sophistication of the type system. Gradual type system designers need more formal tools to help them conceptualize, structure, and evaluate their designs. Based on an understanding of gradual types as abstractions of static types, we have developed systematic foundations for gradual typing based on abstract interpretation, called Abstracting Gradual Typing (AGT for short). Gradual languages designed with the AGT approach satisfy, by construction, the established criteria for gradually-typed languages. In this talk, I will give a brief introduction to AGT in a simply-typed setting, and will then discuss recent work on a gradual counterpart of System F that enforces relational parametricity, even in the presence of imprecise types.