On 15 October 2013, Martínez transferred to Championship side Sheffield Wednesday on an emergency 28-day loan agreement. On 14 November 2013 Arsenal announced that the loan agreement had been extended until 1 January 2014. Martínez made his debut for Wednesday on 23 November 2013 against Yorkshire rivalsHuddersfield Town. The loan was extended to the end of the season soon after.
Fringe Appearances
Martínez was an unused substitute as Arsenal won the Community Shield on 10 August2014, with a 3–0 win over Manchester City at Wembley Stadium. He made his Arsenal debut in the Champions League group stage match against Anderlecht, which ended in a 2–1 win to Arsenal. He then made his Premier League debut as a 2nd half substitute, replacing the injured Szczęsny against Manchester United at the Emirates Stadium. Because of the injuries of Szczęsny and David Ospina, Martínez was made starting keeper against Borussia Dortmund on 26 November at the Emirates, keeping a clean sheet as Arsenal won 2–0. His "faultless" performance in the match led to him being named in that week's UEFA team of the week. He made his first Premier League start on 29 November against West Brom, which was followed by his second Premier League start against Southampton just four days later. He kept two clean sheets as Arsenal won both matches 1–0.
On 20 March 2015, Martínez joined Championship club Rotherham United on an emergency loan until the end of the season. He made his debut the following day against South Yorkshire rivals Sheffield Wednesday, conceding two added-time goals in a 3–2 home defeat.
On 2 August 2017, he was loaned to La Liga side Getafe CF on a one-year deal.
Loan to Reading
On 23 January 2019, he was loaned to Championship side Reading until the end of the season. He made his debut on 29 January against Bolton. A few days later he won man of the match against Aston Villa.
Breakthrough as a Starter
With Bernd Leno being taken off injured during the first half of Arsenal's defeat to Brighton on 20 June 2020, Martinez came off the bench to make his first Premier League appearance since the 2016-2017 season. This led to Martinez seeing out the season as first choice goalkeeper at the club and was highly commended for a string of stellar performances, with Arsenal legend Ian Wright describing him as commanding and as having played brilliantly during this spell in the team. He was very impressive in wins over Wolves, Liverpool and Manchester City. On 1 August 2020, Martinez was selected to start in the FA Cup Final against Chelsea, he went on to make some crucial saves to help Arsenal win their 14th FA Cup, and was visibly emotional and in tears during his post-match interview.
International career
He was called up to the Argentina senior squad to replace Óscar Ustari to face Nigeria in June 2011. He received his second senior call up against Germany and Ecuador on 9 and 13 October 2019, he was an unused substitute for both friendly matches.