Born in Santiago, Vargas grew up in Renca, and began his career playing for Internacional de Renca's youth setup.[2] He also had trials at Universidad Católica and Palestino before taking part of Deportes Puerto Montt's youth categories. In 2005, he was invited to a reality show headed by Adidas, called Adidas Selection Team, and despite not winning the competition,[3] he impressed enough to start the 2006 pre-season trialling with Puerto Rico Islanders, as the club was in Chile.[4]
Vargas made his first team debut on 23 July 2006, aged just 16, playing the last 20 minutes in a 4–1 away loss against Puerto Montt.[8] He appeared in three more matches during the season, all from the bench. After only five further appearances in 2007, he became a regular starter in 2008,[9] scoring his first professional goal on 16 March in a 3–2 home defeat of Palestino.[10] On 30 August, he scored a brace in a 4–3 away win against the same opponent.[11]
Vargas established himself as a starter in 2009, contributing with four goals in 23 appearances.
Universidad de Chile
On 7 January 2010, Vargas joined Universidad de Chile for a US$700,000 transfer fee.[12] He made his debut for the club on 25 January, replacing Gabriel Vargas and scoring the last in a 5–1 home routing of Cobresal.[13]
Vargas only broke into the first team during the 2011 campaign, and had a brilliant performance during the year, scoring 29 goals and providing in 51 matches.[14] He also won both league semestral tournaments (Torneo Apertura and Torneo Clausura), as well as the Copa Sudamericana, where he was the edition's top-scorer and netted goals in both final legs against LDU Quito, scoring the only goal at Casa Blanca and twice in the 3–0 win at the Estadio Nacional in Santiago.[15]
In December 2011, Italian club Napoli purchased the player for a reported US$17.9 million (£11.5 million).[17] On 23 December 2011, Napoli club president Aurelio De Laurentiis, announced Vargas would arrive at the club: "I would like to inform you officially that we purchased Vargas, a few minutes ago I received a call from Dr. De Nicola, who visited the footballer and gave his okay under medical and athletic profile. We signed the contract and we also won the competition by strong Club who wanted the player. This is the testimony that our observatory is always open and we are continuously looking for young talents in the world that can make the case of Napoli and for the growth of our team."[18] Vargas arrived at Napoli on 6 January 2012 and signed on 9 January.[19] He made his debut in a 2–1 Coppa Italia defeat of Cesena at the Stadio San Paolo on 12 January.[20] On 20 May, he was an unused substitute as Napoli defeated Juventus in the Coppa Italia Final at the Stadio Olimpico.
On 20 September 2012, in the first match of Napoli's UEFA Europa League campaign, Vargas scored his first Napoli goals, netting three in a 4–0 victory against AIK.[21] This was the first time that a Chilean player had scored a hat-trick in a continental competition in Europe.
Grêmio (loan)
On 17 January 2013, Vargas agreed to go on loan to Brazilian side Grêmio.[22] He made his first appearance six days later in a Copa Libertadores match against LDU Quito. He scored his first goal on 21 February against Fluminense in the Copa Libertadores. On 31 March, he scored his first goal in the Campeonato Gaúcho, converting a penalty at the Arena do Grêmio in a 1–1 draw with Passo Fundo.
Valencia (loan)
On 23 January 2014, Vargas joined La Liga club Valencia on loan for the rest of the 2013–14 season.[23] Vargas played his first official match for Los Che in a 3–2 away win at Camp Nou against champions Barcelona on 1 February 2014. He scored his first La Liga goal against Real Betis, in a 5–0 home win.[24]
Vargas recorded two goals and three assists in eight appearances as Valencia reached the semi-finals of the 2013–14 UEFA Europa League.[25]
On 22 March 2015, Vargas scored his first goal in five months in QPR's 1–2 home defeat to Everton.[30] He also scored in the team's 4–1 victory at West Bromwich Albion on 4 April, but injured his knee ligament in that match, ruling him out for the remainder of the season.[31] The season ended with QPR finishing bottom of the league, resulting in their relegation to the Championship.
Hoffenheim
On 24 August 2015, Vargas joined German Bundesliga club 1899 Hoffenheim on a four-year deal, for a reported fee of €5 million, plus an additional percentage of any sell-on fee.[32][33]
In September 2013, Vargas broke the Chile national team record for goals in consecutive matches – previously held jointly by Marcelo Salas and Carlos Caszely – by scoring twice in a 2–2 friendly draw with Spain.[15] During 2013, he scored in six consecutive matches and nine times overall for La Roja.[15]
2014 World Cup
On 1 June 2014, Vargas was named by Jorge Sampaoli in Chile's 23-man squad for the 2014 World Cup in Brazil.[39] In Chile's second group match, against defending champions Spain at the Maracanã Stadium, Vargas scored the team's opening goal as they mathematically eliminated Spain and secured qualification to the knockout stage.[40]
2015 Copa América
On 11 June 2015, Vargas scored for Chile in the opening match of the 2015 Copa América, a 2–0 win over Ecuador at the Estadio Nacional in Santiago.[41] In the team's next fixture, Vargas scored his second goal of the tournament, heading an equalizer as the hosts drew 3–3 with Mexico on 15 June.[42] In the semi-final against Peru, Vargas scored both goals in a 2–1 victory for Chile, the second of which was a long-distance effort, to send La Roja to the final. Although Vargas was substituted out in extra time, Chile won in a penalty shootout against Argentina to win their first major international honour.[43] Vargas' four goals made him the competition's joint top scorer alongside Peruvian Paolo Guerrero, and he was named in the Team of the Tournament.[44]
Copa América Centenario
On 14 June 2016, at the Copa América Centenario, Vargas and Alexis Sánchez scored twice each in a 4–2 win over Panama in Philadelphia to qualify for the quarter-finals of the tournament.[45] Four days later, he added four more goals at Levi's Stadium in a 7–0 rout of Mexico.[46] Chile retained their title with another win on penalties against Argentina, and Vargas was again the top scorer with six goals.[47]
Despite his previous successes with the national team, Vargas, along with Marcelo Díaz, fell out of favour following the appointment of Reinaldo Rueda in 2018 and made only a single friendly appearance for Chile in the year.[48]
2019 Copa América
Vargas was included in Chile's 23-man squad for the 2019 Copa América in Brazil. He scored twice against Japan in a 4–0 win for Chile's opening match.[49]
2021 Copa América
Vargas scored two goals in the 2021 Copa América, one each against Argentina and Uruguay, which both ended in a 1–1 draw. On 2 July 2021, Vargas played his 100th match for Chile in a 1–0 defeat against Brazil in the quarter-finals.[50]
^"Cobreloa "B" no pudo en Arica" [Cobreloa "B" could not handle Arica] (in Spanish). El Mercurio de Calama. 28 August 2006. Archived from the original on 4 March 2016. Retrieved 10 January 2019.