He graduated in 1987 at the Faculty of Applied Arts in Belgrade.
His works were acknowledged early during his studies, and were published in student magazines Student (1982) and Vidici (1982).
In early eighties he became known as a Science Fiction and Fantasy illustrator. His illustrations were published on the covers of novels of "Znak Sagite" imprint, Science Fiction and Fantasy Almanac "Monolit" and magazine "Alef", later in Politikin Zabavnik.
His career shifted to artwork for children, in magazines "Tik-Tak" and "Zeka" (1987–1998). He created a popular children's comic strip Jajzi that ran in "Tik-Tak". His true breakthrough came as he became a regular illustrator for "Politikin zabavnik".
In late nineties Živković was Art Director and premier illustrator of Saatchi & Saatchi offices in Serbia and Slovenia. He continues working in advertising business as well as a freelancer illustrator.
He is a promoter of environment awareness, children's rights, and often draws for humanitarian non-profits.
Most of his work in the last two decades was for "Creative Centre" publishing house (more than hundred books, translated into over 40 languages), and helped build their recognizable brand.
- Cover of Serbian edition of Tolkien’s "Lord of the Rings" (Fellowship of the Ring, The Two Towers, Return of the King)
- Cover for Serbian edition of Stephen King’s "It"
- "National park Serbia", with Dragoljub Ljubičić
- "Sex for beginners", with Jasminka Petrović (sample)
- "School", with Jasminka Petrović (sample)
- Belgrade Zoo — "Good Hope Garden" campaign
- "Smart Book for Mum and Dad" for Serbian UNICEF  (in Serbian and English)
- Three “Lazar Komarčić” awards for best science-fiction related artwork (1985, 1986. and 1988.)
- Five “Neven” awards for best illustrated children's book (given by “Prijatelji dece Srbije”, a children’s rights organisation)
- Two “Zlatno pero Beograda” Awards (an award given by ULUPUDUS, An Assosciaton of visual and applied artists and designers)
- Nominated for 2011 Hans Christian Andersen Award given by IBBY