What happens if there are conflicts between changes made by multiple users?

Scrumwise handles all conflicts automatically in the background, without ever bothering you. The result will be what you expect. But typically, conflicts don't happen very often, since Scrumwise shows you if somebody else is editing a field or making other changes to something, while it happens, so you can easily avoid making conflicting changes. But if you do, it won't be a problem, and the result will feel natural.