A federal judge on Tuesday permanently blocked Alabama from executing an inmate with nitrogen gas after declaring the method violates the ban on cruel and unusual punishment. States have various execution methods, including lethal injection, electrocution, lethal gas and firing squad. Lethal injection is the primary method in most states, but it has faced issues including drug shortages and botched executions. Some states are exploring alternatives like firing squads. The federal appellate court's decision highlights ongoing debates about execution methods and their constitutionality.