Date of this Version
Published (2022) Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of his 75th Birthday, pp. 343-371.
We survey old and new approaches to the study of symbolic powers of ideals. Our focus is on the symbolic Rees algebra of an ideal, viewed both as a tool to investigate its symbolic powers and as a source of challenging problems in its own right. We provide an invitation to this area of investigation by stating several open questions.