Reorder tasks

I can't figure out how to reorder tasks by dragging and dropping them in the Board view. Honestly, I can't figure out any way to reorder them at all, on any view, except for changing how the tasks are sorted. That does not help me at all, as priorities are always changing and I need to be able to move the most important tasks to the top (marking them high importance doesn't help, as many are high importance at any time). I've never seen a PM software that doesn't allow this. There's got to be a way. Any suggestions? If it's just not possible, could you confirm that it's not possible?