The Textile Workers Union (the union) (plaintiff) and Lincoln Mills (the employer) (defendant) had a collective-bargaining agreement that mandated arbitration of grievances between the employer and employees. The union sued the employer in federal court to compel the employer to participate in grievance arbitrations. The suit was brought under § 301 of the Taft-Hartley Act, 29 U.S.C. § 185(a), which grants jurisdiction to federal courts in actions involving labor-management contracts in industries affecting commerce. The district court ruled that federal jurisdiction was proper and compelled the employer to participate in arbitration. The United States Court of Appeals for the Fifth Circuit reversed, agreeing that jurisdiction was granted under the statute, but ruling that the district court had no authority under federal or state law to grant substantive relief. The union appealed, and the United States Supreme Court granted certiorari.