Recorded as part of the Quantum and Thermal Electrodynamic Fluctuations in the Presence of Matter: Progress and Challenges conference at KITP (July 11-14, 2022) in Santa Barbara, CA. This conference will explore many aspects of classical and quantum fluctuating electromagnetic fields in the presence of matter, which impact a wide range of fundamental and practical phenomena in domains of physics, chemistry end engineering. Building upon the significant milestones achieved in the realms of the Casimir interactions between bodies, and the role of quantum field fluctuations in heat transfer in the near- and far-fields, we plan to address a plethora of novel questions and remaining puzzles: the ramifications of 2D (topological) and non-reciprocal materials, the possibility of detecting quantum friction, the discord between different experimental and theoretical results. Unraveling these puzzles will have profound impacts from fundamental science to novel applications of materials. The conference will bring together theorists and experimentalists who will address unsettled topics and possible new experimental directions that could elucidate them.