This paper is a write-up of the ideas that were presented, developed and discussed at the third International Workshop on QCD Challenges from pp to A-A, which took place in August 2019 in Lund, Sweden. The goal of the workshop was to focus on some of the open questions in the field and try to come up with concrete suggestions for how to make progress on both the experimental and theoretical sides. The paper gives a brief introduction to each topic and then summarizes the primary results.