Diverged branches occur when a local branch and its remote counterpart have different histories. Recognizing divergence is crucial, and ways to do so include git status, git push, or git pull. Resolving divergence depends on the situation. One approach is to keep both changesets by using git pull --rebase. To discard remote changes, use git push --force, but use git push --force-with-lease for added safety. Alternatively, to overwrite local changes, use git reset --hard origin/main. These solutions provide options for resolving divergence based on workflow and situation.