Is it possible to classify explicitly compact 2-dimensional Alexandrov spaces with curvature bounded below (either with or without boundary)?

If yes, a reference would be helpful.

**EDIT:** If the question is too general, may be one can classify somehow non-negatively curved compact 2-dimensional Alexandrov spaces, e.g. as pieces of convex surfaces (see my comment below). In general I would be interested to know as precise result as possible.