Milkhemet Mitzvah (Hebrew: מלחמת מצווה, "War by commandment") is the term for a war during the times of the Tanakh when a king (of the Kingdom of Israel) would go to war in order to fulfil something based on, and required by, the Torah without needing approval from a Sanhedrin, such as war against Amalek.
Unlike milkhemet reshut wars, which tended to be fought to expand territory or for economic reasons and had exemption clauses, milhemet mitzvah tended to be invoked in defensive wars, when vital interests were at risk.
The notions, terms and functions of milkhemet mitzvah and milkhemet reshut were classically only utilized in the times of the Kingdoms of Israel and Judah. The milchemet reshut has not been applied or used since then; because the Jewish people have neither a king nor universally recognized Sanhedrin, there is no religious authority to authorize a milchemet reshut.
Some modern rabbis, especially in the Religious Zionist camp, consider service in the Israel Defense Forces to be permissible (or even laudable) by categorizing the IDF's military operations as falling under the self-defense-type milchemet mitzvah.
The modern, officially secular, nation-state of Israel does not base its military and strategic decisions on these concepts and considerations.