Still without an answer or an ending. An unresolved problem has not been fixed; an unresolved question has not been answered; an unresolved argument is still hanging in the air. The key feeling is that the matter is not closed and is still sitting there, waiting. It is used for concrete things (an unresolved dispute between two companies, an unresolved case at the police station) and for feelings (unresolved anger, unresolved grief, unresolved issues between a parent and a child). That second use is very common in everyday talk about relationships and therapy: 'they have a lot of unresolved stuff' means old trouble nobody dealt with. It is a mildly formal word but not a rare one — news reports and ordinary conversation both use it. In computing it has its own life: an unresolved link or unresolved reference means the computer could not find what a name points to. Notice it usually comes before a noun; 'the problem remains unresolved' is the common way to use it after a verb.