Peirce's theory of assertions articulates the original commitment theory of assertions. Commitment theories of assertion have gained considerable recent interest not only in the Peirce scholarship but also in studies of history and philosophy of language, logic and communication. In this preface we point out some recent work on the topic and provide a brief introduction to the papers published in this Transactions symposium. These papers consist of a selection of those presented in the workshop "Peirce on Assertion" held in Lecce, Italy, on 13 September 2019.