Over 35 EuroLeague games played that season, Reyes averaged 8.4 points and 4.3 rebounds per game. On 4 February 2019, Reyes became the ACB League's all-time leader in games played, including both formats of the league (ACB & Primera División). He achieved that after he played in his 779th Spanish League game, against Unicaja Málaga, eclipsing the league's previous record-holder for most games played, Joan Creus's tally. On 15 February 2019, Reyes became the all-time leader in games played in the Spanish King's Cup tournament, as he overtook Juan Carlos Navarro, to achieve that record. Reyes was a member of the junior national teams of Spain. With Spain's junior national teams, he won medals at the following tournaments: the gold medal at the 1998 FIBA Europe Under-18 Championship, the gold medal at the 1999 FIBA Under-19 World Cup, and the bronze medal at the 2000 FIBA Europe Under-20 Championship. Reyes was a long-time member of the senior Spanish national team. With Spain's senior national team, he won the following medals: the bronze medal at the 2001 EuroBasket, the silver medal at the 2003 EuroBasket, the gold medal at the 2006 FIBA World Cup, the silver medal at the 2007 EuroBasket, the silver medal at the 2008 Summer Olympics, the gold medal at the 2009 EuroBasket, the gold medal at the 2011 EuroBasket, the silver medal at the 2012 Summer Olympics, the gold medal at the 2015 EuroBasket, and the bronze medal at the 2016 Summer Olympics. With Spain, he also played at the 2002 FIBA World Cup, the 2004 Summer Olympics, the 2005 EuroBasket, the 2010 FIBA World Cup, and the 2014 FIBA World Cup. Reyes' older brother, Alfonso, is also a former professional basketball player. Reyes' nickname is "Espartaco" (English: "Spartacus").