What Are the Most Important Open Problems in Concurrency?

Let us assume that one can assess the healthiness of a research field, say concurrency theory, by looking at the most important open problems in that field. These open problems can be used to try and convince researchers in another area and students that the field of concurrency theory is "alive and kicking", and maybe entice a few of them to work within the field.

Based upon this thought experiment, wouldn't it be a good thing to have a repository of open problems that identify the present state of development in concurrency theory, and suggest directions for further research?

At some point in the past, I started putting together a list of open problems, but I have not really maintained it for a while. Will you help me revive this enterprise by sending me, or posting as a comment to this blog entry, a description of your favourite open problems in concurrency theory, together with links to partial solutions and pointers to the literature? This input of yours might even form the basis for a useful installment of the Concurrency Column in the Bulletin of the EATCS, and generate a lot of research in our field following what Luca Trevisan has called in this very informative blog entry the "Hungarian approach to mathematics": pose very difficult problems, and let deep results, connections between different areas of math, and applications, come out as byproducts of the search for a solution.

By the way, Luca Trevisan has a few very interesting posts related to Szemeredi's theorem and other results in additive combinatorics. (See this one, and the five blog entries on Szemeredi's theorem.) Those posts give an inkling of the level of mathematical sophistication that has been reached in TCS research from the volume A camp. Check them out!