Maxi Rodriguez

In 2002, Rodríguez moved to La Liga to join RCD Espanyol, his league debut coming on 2 September in a 0–2 loss against Real Madrid. He played 37 matches in every campaign with the Catalans, scoring 15 goals during his last.

Rodríguez won the 2001 FIFA World Youth Championship with the Argentine under-20s on home soil, scoring four goals in seven matches including the first and last for the eventual winners. He made his full side debut in a friendly match against Japan on 8 June 2003, in which he also found the net.

After Argentina lost the quarter-final game against Germany on 30 June 2006, Rodríguez punched opponent Bastian Schweinsteiger in the back. FIFA fined him CHF5,000 and suspended him from two matches in the 2007 Copa América for violent conduct. However, after a serious knee injury in a friendly with Spain in October 2006, he missed the continental competition as national team manager Alfio Basile, whom initially intended to select the player, eventually rested him for precaution.

On 10 November 2009, Rodríguez put four goals past UD Marbella in the Copa del Rey round-of-32 second leg, in an eventual 6–0 home win (8–0 aggregate). After the 2007 departure of Fernando Torres to Liverpool, he was selected as the new club captain; he took no part in the Colchoneros' 2009–10 UEFA Europa League campaign, which ended in conquest.

In 2009, Rodríguez appeared in a music video for Coti, starring alongside Atlético teammate Diego Forlán.

On 13 January 2010, Rodríguez completed a free transfer to Liverpool, signing a three-and-a-half-year deal. After securing his signature, Rafael Benítez described him as "comfortable on the ball, can pass and keep possession. He is good at getting into the box and scoring goals and a good finisher", and the player was given the number 17 shirt, making his debut for the club as a second-half substitute in a Premier League match against Stoke City on the 16th; his first full start came a week and a half later, in a 0–0 away draw to Wolverhampton Wanderers.

In his first games for Liverpool, Rodríguez picked up two league assists, both of which were for former Atlético teammate Torres. He scored his first competitive goal in a 4–0 win over Burnley at Turf Moor on 25 April 2010, playing the full 90 minutes.

Rodríguez scored in Diego Maradona's first game in charge of Argentina, a 0–1 friendly win in Scotland. On 19 May 2010 he was named in the squad of 23 for the 2010 World Cup in South Africa and, in the last home game before the finals five days later, scored twice against Canada, netting from a freekick from a sharp angle and after receiving a pass from Carlos Tevez in an eventual 5–0 win.

On 8 July 2011, Rodríguez switched his jersey number to 11, and he scored two goals in a pre-season friendly with Malaysia shortly after, which finished with a 6–3 win. On 24 August, he was given his first start of the season in a League Cup tie against Exeter City, and netted the second in an eventual 3–1 away success.

On 20 November 2011, Rodríguez scored against Chelsea following a build-up with teammate Craig Bellamy, with Liverpool winning it 2–1 at Stamford Bridge. Nine days later, against the same opponent, in the same venue and again with the decisive pass being made by the Welshman, he found the net in a 2–0 League Cup triumph, and his team went on to win the latter competition.

On 26 December 2011, Rodríguez scored just his second league goal of the season in a 1–1 draw at Anfield against Blackburn Rovers. He netted his last two against the same adversary on 10 April 2012, for a 3–2 away win.

On 13 July 2012, after 73 official games and 17 goals scored, Rodríguez left Liverpool and returned to his first professional club Newell's Old Boys. He wrote an open letter to the Reds fans before his departure, thanking them for their support in his two-and-a-half-year stint.

Rodríguez played his first match for the club since leaving on 5 August 2012, in a 0–0 draw against Club Atlético Independiente. According to him, football in his country was now "worse than ten years ago". In June 2013, he helped the team win the Torneo Final, being awarded the Alumni by directors and former directors of Argentinian football late in the year.

In June 2014, Rodríguez made Argentina's list for the 2014 World Cup. He started in his side's opening game, a 2–1 defeat of Bosnia and Herzegovina at the Estádio do Maracanã, playing the first half before being substituted for Gonzalo Higuaín at half-time; he was only fielded again in the semi-finals against the Netherlands, converting the decisive penalty shootout attempt (0–0 after 120 minutes) to send his country to the final for the first time in 24 years.

In July 2017, 36-year-old Rodríguez moved to Uruguayan club Peñarol. After winning the league in both of his seasons in Montevideo, he returned to Newell's on an 18-month contract in the last days of 2018.