1. UEFA Champions League Triumph: One of the most notable achievements during this period was Real Madrid's success in the UEFA Champions League. In the 1997/1998 season, under the management of Jupp Heynckes, Real Madrid secured their seventh European Cup/Champions League title by defeating Juventus 1-0 in the final. Predominantly remembered for Predrag Mijatović's solitary goal, this victory marked a return to European glory for the club.

2. Domestic Success: Real Madrid also experienced success domestically during the 1998/1999 and 1999/2000 seasons. In 1999, they clinched the La Liga title under the guidance of manager Guus Hiddink. This triumph was followed by another La Liga title win in the 2000/2001 season under the management of Vicente del Bosque. These domestic triumphs further solidified Real Madrid's status as a dominant force in Spanish football.

3. Squad and Key Players: Real Madrid boasted a talented squad during this period, featuring iconic players such as Raúl González Blanco, Fernando Hierro, Roberto Carlos, and Clarence Seedorf. These players played pivotal roles in the team's success, contributing with their skill, leadership, and determination on the pitch. Additionally, the club made notable signings during these seasons, including Luís Figo from Barcelona in 2000, further strengthening the team.

4. Copa del Rey Victory: In addition to their Champions League and La Liga triumphs, Real Madrid also secured success in the Copa del Rey during this period. In the 1999/2000 season, they won the Copa del Rey by defeating Valencia 3-0 in the final. This victory added another piece of silverware to Real Madrid's trophy cabinet and highlighted their dominance across multiple competitions.

5. Managerial Stability: Real Madrid benefited from managerial stability during this period, with managers such as Jupp Heynckes, Guus Hiddink, and Vicente del Bosque providing continuity and strategic direction to the team. Their leadership played a crucial role in guiding Real Madrid to success both domestically and in European competitions.

Overall, the 1998/1999 and 1999/2000 seasons were remarkable periods for Real Madrid, characterized by triumphs in the UEFA Champions League, La Liga, and the Copa del Rey. The team's success during this time solidified their reputation as one of the most prestigious and successful clubs in European football history.