This bill, titled the "No Nuclear Testing Without Approval Act," establishes a requirement for explicit Congressional approval before the United States can conduct any explosive nuclear testing. It amends the Atomic Energy Defense Act to prohibit such testing unless specific conditions are met. These conditions include either a foreign state conducting an explosive nuclear test or a demonstrated technical need for testing. Before any testing can proceed, the President must submit a detailed notification to Congress at least 180 days in advance. This notification must describe the proposed testing, state the reasons, assess alternatives if for technical need, and estimate timelines and costs. Ultimately, a joint resolution approving the testing must be enacted into law. The approval process varies based on the reason for testing. If testing is proposed in response to a foreign nuclear test, the joint resolution requires a two-thirds affirmative vote in the Senate. For testing driven by a technical need concerning nuclear weapon safety or reliability, the bill outlines expedited legislative procedures in both the House and Senate, but still mandates a two-thirds Senate vote for passage. The bill also defines explosive nuclear testing to exclude subcritical experiments and certain fusion research.