Final answer:
The most common method of execution in the United States is lethal injection, with Utah still allowing the use of a firing squad. The death penalty remains a contentious issue, with concerns over cruel and unusual punishment and wrongful executions influencing its application.
Step-by-step explanation:
The question is about the methods of execution used in the United States and which states continue to use them. Lethal injection is currently the most common form of execution in the US, but various methods are still used in certain jurisdictions, reflecting ongoing controversies about the death penalty and its constitutionality related to the Eighth Amendment and the concept of cruel and unusual punishment.
The state of Utah continues to allow the use of a firing squad if lethal injection drugs are not available. This is noteworthy particularly because of the recent case where a death-row inmate requested to be executed by firing squad instead of lethal injection, which was rejected. The death penalty continues to be a topic of significant legal debate and has seen a decline in application partly due to concerns over wrongful executions and evolving public opinion.