In previous articles, I have written about how I organize my own personal productivity. However, many of my projects are collaborative, and physical paper doesn't work very well for sharing task lists.
I don't have a super-rigorous system for managing collaborative projects, particularly since they also depend on collaborators. We do find Trello useful for a number of projects, but its effectiveness does depend on everyone keeping it updated. An out-of-date Trello can be somewhat useful, but rapidly becomes a place that just tracks project components and doesn't provide anyone with insight into project status.
I use GitHub Issues for tracking to-do work on open-source software like LensKit; that works out pretty well.
For some projects, we just use Google documents (or occasionally spreadsheets). It all depends on what works well enough with the project (and people) that it gets updated and remains useful.
I do want to make it clear that I am not criticizing my colleagues when discussing the drawbacks of tools not being updated. The tools need to work with us and for us, not the other way around.