Unndór graduated with a Bachelor's degree from the Iceland University of the Arts in 2008 and earned a Master of Fine Arts degree from Valand Academy in Gothenburg in 2011. Unndór has been actively participating in exhibitions both in Iceland and abroad since his graduation. Some notable group exhibitions include "Momentu Design" at Momentum Arthall in Moss, Norway, in 2010, "Ríki, flóra, fána, fabúla" at Reykjavik Art Museum in 2016, "Cloudbusters: Intensity vs. Intension" at the Estonian Museum of Contemporary Art in Tallinn, Estonia, in 2018, and solo exhibitions like "Tvívængja" at Nýlistarsafnið in 2015 and "Cul de Sac" at Kling og Bang Gallery in 2020.