How can you overturn a criminal conviction?

Despite what many might think, miscarriages of justice do happen and there are probably more unsafe convictions than the criminal justice system is keen to accept. People who experience this are left wondering what they can do?
Those who have fought to clear their names or the name of a loved one know the process takes time, can be complex and frustrating. But the criminal justice system is meant to ensure that if a miscarriage of justice has taken place it can be corrected.