Abstract: This Introduction to the collection of essays surveys the philosophical literature to date with respect to five central questions: justice, care, agency, metaphilosophical issues regarding the language and representation of cognitive disability, and personhood. These themes are discussed in relation to three specific conditions: intellectual and developmental disabilities, Alzheimer's disease, and autism, though the issues raised are relevant to a broad range of cognitive disabilities. The Introduction offers a brief historical overview of the treatment cognitive disability has received from philosophers, and explains the specific challenges that cognitive disability poses to philosophy. In briefly summarizing the essays in the collection, it highlights the distinctive contributions the collection makes to ethics, political philosophy, bioethics, and the philosophy of disability. We hope that the richness of the topics explored by these essays will be a spur to further investigation.