[6] Víkingur's album Philip Glass Piano Works saw him named "Iceland's Glenn Gould" by the New York Times,[7] and a "breathtakingly brilliant pianist" by Gramophone;[8] Le Monde heralded his "volcanic temperament, great virtuosity, taste for challenges".

[10] He later studied with Erla Stefánsdóttir and Peter Máté before attending the Juilliard School in New York, earning bachelor's and master's degrees under the supervision of Jerome Lowenthal and Robert McDonald.

[15] In the same season, Víkingur was artist-in-residence at the Konzerthaus Berlin, with fourteen performances over eleven different projects, playing concertos by Adès, Robert Schumann, Daníel Bjarnason, and Mozart, two solo recitals, and chamber programmes with Martin Fröst and Florian Boesch.

Víkingur has premiered six piano concertos by Icelandic composers—including Snorri Sigfús Birgisson [is],[16] Daníel Bjarnason,[17] Haukur Tómasson,[18] and Þórður Magnússon [is][19]—as well as solo and chamber works by Atli Ingólfsson,[20] Mark Simpson,[21] and Mark-Anthony Turnage.

[22] He has taken part in collaborative performances with Philip Glass (in Reykjavík,[23] Gothenburg,[24] and London[25][26]) and Björk, the latter on the television programme Átta raddir, produced by Jónas Sen for RÚV, the Icelandic National Broadcasting Service.

[46] At the 2014 Transart Festival in Bolzano, Italy, Víkingur collaborated with Swiss artist Roman Signer in an event titled Vers la Flamme – Ein Konzert mit Störung.