Greiss is a native of Füssen, Germany. As a youth, he played in the 1999 Quebec International Pee-Wee Hockey Tournament with a team from Munich. He developed through the youth ranks of EV Füssen before heading to the Kölner Haie organization in 2002. He made his debut in the German top-flight Deutsche Eishockey Liga for the Cologne-based team during the 2003–04 campaign. The San Jose Sharks selected Greiss in the third round, 94th overall, in the 2004 NHL Entry Draft. Greiss played for San Jose during the Sharks' pre-season games ahead of the 2007–08 season, though he was eventually assigned to the team's then-American Hockey League affiliate, the Worcester Sharks. On 8 January 2008, he was recalled to replace German compatriot Dimitri Pätzold as the backup goaltender to Evgeni Nabokov. Greiss started his first career NHL game on 13 January 2008, an eventual 4–3 overtime loss to the Anaheim Ducks. For the 2009–10 season, he served as the back-up goaltender to starter Nabokov. in 2009 On 12 October 2010, just prior to the commencement of the 2010–11 season, Greiss was put on waivers by San Jose, eventually clearing and reporting to Worcester of the AHL. Greiss' demotion was in large part due to the off-season signings of Finnish goaltenders Antero Niittymäki and Antti Niemi. Nine days later, after failing to see any gameplay as Worcester's third-string goaltender, he was reassigned to Brynäs IF in the Swedish Elitserien to provide him regular playing time. In April 2011, Greiss was recalled from Brynäs to San Jose for the team's run in the 2011 Stanley Cup playoffs. He later re-signed with the Sharks on 7 July. For the Sharks' 2011–12 season opener, Greiss was the team's starter in a 6–3 win over the Phoenix Coyotes in San Jose. He went on to start the next two games—losses to the Anaheim Ducks and St. Louis Blues—before Antti Niemi returned from off-season surgery. Later in the season, Greiss recorded his first career NHL shutout on 26 January 2013, recording 24 saves in a 4–0 win over the Colorado Avalanche. Greiss became a free agent in July 2013 and subsequently signed a one-year contract with the Phoenix Coyotes. In his only season with Phoenix, he played in 25 games, posting a 2.25 goals against average and.920 save percentage. At the end of the 2013–14 season, he was not re-signed by the Coyotes, whereupon he signed a one-year, $1 million contract as an unrestricted free agent with the Pittsburgh Penguins on 1 July 2014. After the 2014–15 season in which he appeared in 20 games for the Penguins, Greiss once again switched teams as a free agent, signing with the New York Islanders on a two-year, $3 million contract. In March 2016, Jaroslav Halák, the Islanders' starting goaltender, suffered a lower-body injury sidelining him six weeks, leaving Greiss as the team's temporary starter. In December 2016, the Islanders waived Halák, leaving Greiss and Jean-François Bérubé as the Islanders' two goaltenders. On 30 January 2017, Greiss signed a three-year contract extension with the Islanders. On 15 January 2018, Greiss made a career-high 52 saves in a 5–4 overtime win over the Montreal Canadiens.
International play
In 2006, Greiss earned a roster spot on the German team for the 2006 Winter Olympics; at just 20 years of age, he was the youngest goaltender in the tournament. During the tournament, Greiss notably recorded an impressive 35-save performance against Canada. Greiss was again named to the German squad for in the 2010 Winter Olympics in Vancouver.
Personal life
Greiss' wife Brittany was Miss South Dakota USA in 2014. Together, they have a daughter.