Science and technology are embedded in every aspect of modern life. This report describes how Public Engagement with Science (PES), in the context of informal science education (ISE), can provide opportunities for public awareness of and participation in science and technology. PES refers to seeking public input into policy decisions about the development and application of science and technology in society. The implementation of PES in the science policy arena has helped to develop and articulate new understanding of and expectations for the relationship between science and publics in policy making and other contexts. In response to a request by the National Science Foundation, the Center for Advancement of Informal Science Education (CAISE) established a CAISE PES Inquiry Group to: (1) assemble and articulate the concepts, issues, tensions, and context of PES as it relates to informal science education; (2) broaden the conversation about PES to include a larger and more diverse pool of ISE professionals and stakeholders, including funding agencies, the scientific community, and ISE evaluators and researchers; and (3) expand the range of current ISE activities by promoting the use and study of PES in informal science education. This CAISE Inquiry Group Report seeks to serve as a prompt for discussion and exploration of PES in ISE. The goals in writing this report are to open up the conversation up further, to foster dialogue and interaction across the communities, to intentionally build on one another's work, and to push the boundaries of what PES in ISE could mean as well as to improve its effectiveness and impact. Appended are: (1) Pushing Boundaries: Strategies for Including PES in ISE; (2) Commonly Used Terms Describing Public and Science Activities; (3) PES and Learning; (4) Potential Impacts of PES-based ISE Projects; (5) Descriptions of PES Case Studies; (6) ISE Project Survey; (7) Dimension of the ISE Spectrum: PUS to PES; and (8) Motivations for Why Scientists Get Involved with PES in ISE. (Contains 4 figures, 2 tables and 16 footnotes.) [For "Many Experts, Many Audiences: Public Engagement with Science and Informal Science Education. A CAISE Inquiry Group Report. Executive Summary," see ED536432.]