The discussion on the current status of constructive quantum field theory (QFT) reveals that significant progress has not been made since Rivasseau's 2000 review, particularly regarding a full constructive formulation of QFT in four dimensions. While there have been advancements in lower-dimensional field theories, the complexities of renormalization and the need for precise estimates in four dimensions remain major hurdles. Participants express skepticism about the feasibility of achieving a mathematically rigorous continuous field theory, suggesting that existing theories may simply be effective models rather than fundamentally rigorous constructs. The conversation also touches on the philosophical implications of rigor in physics, with some arguing that a lack of rigorous formulation does not undermine the usefulness of a theory. Overall, the consensus is that breakthroughs are needed to advance the field significantly.