Born inSantiago, Vargas grew up inRenca, and began his career playing for Internacional de Renca's youth setup.[2] He also had trials atUniversidad Católica andPalestino before taking part ofDeportes Puerto Montt's youth categories. In 2005, he was invited to a reality show headed byAdidas, calledAdidas Selection Team, and despite not winning the competition,[3] he impressed enough to start the 2006 pre-season trialling withPuerto 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 duringthe 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 ofPalestino.[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.
On 7 January 2010, Vargas joinedUniversidad de Chile for aUS$700,000 transfer fee.[12] He made his debut for the club on 25 January, replacingGabriel Vargas and scoring the last in a 5–1 home routing ofCobresal.[13]
In December 2011, Italian clubNapoli purchased the player for a reported US$17.9 million (£11.5 million).[17] On 23 December 2011, Napoli club presidentAurelio 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 2–1Coppa Italia defeat ofCesena at theStadio San Paolo on 12 January.[20] On 20 May, he was an unused substitute as Napoli defeatedJuventus in theCoppa Italia Final at theStadio Olimpico.
On 20 September 2012, in the first match of Napoli'sUEFA Europa League campaign, Vargas scored his first Napoli goals, netting three in a 4–0 victory againstAIK.[21] This was the first time that a Chilean player had scored ahat-trick in a continental competition in Europe.
On 17 January 2013, Vargas agreed to go on loan to Brazilian sideGrêmio.[22] He made his first appearance six days later in aCopa Libertadores match against LDU Quito. He scored his first goal on 21 February againstFluminense in the Copa Libertadores. On 31 March, he scored his first goal in theCampeonato Gaúcho, converting a penalty at theArena do Grêmio in a 1–1 draw withPasso Fundo.
On 23 January 2014, Vargas joinedLa Liga clubValencia on loan for the rest of the2013–14 season.[23] Vargas played his first official match forLos Che in a 3–2 away win atCamp Nou against championsBarcelona on 1 February 2014. He scored his first La Liga goal againstReal 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 the2013–14 UEFA Europa League.[25]
On 22 March 2015, Vargas scored his first goal in five months in QPR's 1–2 home defeat toEverton.[30] He also scored in the team's 4–1 victory atWest 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 theChampionship.
On 24 August 2015, Vargas joined GermanBundesliga club1899 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 byMarcelo Salas andCarlos 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 forLa Roja.[15]
On 1 June 2014, Vargas was named byJorge Sampaoli in Chile's 23-man squad for the2014 World Cup in Brazil.[40] In Chile's second group match, against defending champions Spain at theMaracanã Stadium, Vargas scored the team's opening goal as they mathematically eliminated Spain and secured qualification to theknockout stage.[41]
On 11 June 2015, Vargas scored for Chile in the opening match of the2015 Copa América, a 2–0 win overEcuador at theEstadio Nacional in Santiago.[42] In the team's next fixture, Vargas scored his second goal of the tournament, heading an equalizer as the hosts drew 3–3 withMexico on 15 June.[43] 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 sendLa Roja tothe final. Although Vargas was substituted out in extra time, Chile won in apenalty shootout againstArgentina to win their first major international honour.[44] Vargas' four goals made him the competition's joint top scorer alongside PeruvianPaolo Guerrero, and he was named in the Team of the Tournament.[45]
On 14 June 2016, at theCopa América Centenario, Vargas and Alexis Sánchez scored twice each in a 4–2 win overPanama inPhiladelphia to qualify for the quarter-finals of the tournament.[46] Four days later, he added four more goals atLevi's Stadium in a 7–0 rout of Mexico.[47] Chile retained their title with another win on penalties against Argentina, and Vargas was again the top scorer with six goals.[48]
Despite his previous successes with the national team, Vargas, along withMarcelo Díaz, fell out of favour following the appointment ofReinaldo Rueda in 2018 and made only a single friendly appearance for Chile in the year.[49]
Vargas was included in Chile's 23-man squad for the2019 Copa América in Brazil. He scored twice againstJapan in a 4–0 win for Chile's opening match.[50]
Vargas scored two goals in the2021 Copa América, one each against Argentina andUruguay, which both ended in a 1–1 draw. On 2 July 2021, Vargas played his 100th match for Chile in a 1–0 defeat againstBrazil in the quarter-finals.[51]
^"Cobreloa "B" no pudo en Arica" [Cobreloa "B" could not handle Arica] (in Spanish). El Mercurio de Calama. 28 August 2006. Archived fromthe original on 4 March 2016. Retrieved10 January 2019.