Zvonar's collage works are composed of source materials drawn from art history, contemporary advertising and popular culture. They question existing social and cultural systems through the use of humour and irony. Her work often speaks to the ethos and aspirations of those on the periphery of mainstream society, drawing inspiration from counterculture movements that challenge the status quo. Zvonar treats imagery as metaphor, establishing a referential context that calls into question popular conceptions and historical canons to address cultural constructions of power. She often uses a feminist perspective to illustrate how rules of engagement were unbalanced in the past and remain so today. Zvonar has exhibited in solo and group exhibitions throughout Canada and in New York, Australia, Japan and Belgium. In 2008, Zvonar was the inaugural artist at the Malaspina Print Research Residency and was an artist in residence at the Banff Centre for the Arts for the thematic residency Cosmic Ray Research. She received the 2009 City of Vancouver Mayor's Arts Award for Emerging Visual Artist; was presented with the 2011 Emily Award for outstanding achievement by an Emily Carr University alum; and was the 2015 recipient of the Shadbolt Foundation's VIVA Award.