His father András Ungár is a sociologist, his mother Mária Schmidt is a historian who is the director of the House of Terror Museum in Budapest.

[11] The 2014 Hungarian local elections saw Ungár receive 291 votes in the 2nd District of Budapest, failing to become the individual constituency's representative.

[15] In 2016, Ungár started to build a media portfolio,[16] his first independent news portal was Reflektor, run through the Fényszóró Média Alapítvány.

In 2018, he conducted serious, but ultimately unsuccessful, negotiations with Lajos Simicska on the acquisition of Magyar Nemzet, Lánchíd Rádió and Heti Válasz.

[19] According to the tax returns of 2018, Ungár had assets of 15 billion HUF (€41 million), which consisted of family businesses and property rights to magazines.