In 1995, he graduated from the American University in Bulgaria with a Bachelor of Arts degree in "Mass Communication and Media Studies".

He supervised the integration of Metromedia's European radio group into Communicorp, and was in charge of the company's further expansion in existing and new markets, such as Ukraine and Latvia.

In 2006, his company RadioCorp B.V. received a broadcasting license in the Netherlands to create a radio station focusing on national music.

[4][3] On 26 December 2022 the Ministry of Internal Affairs of Russia announced that Grozev was on its "wanted" list without disclosing the reason.

[15][16] According to Russian state-owned domestic news agency RIA Novosti, a criminal case was opened against Grozev for "spreading fakes".

RIA cited a law enforcement source as saying Grozev was accused of facilitating the escape of Roman Dobrokhotov, the editor of a Russian news outlet The Insider, who left Russia in 2021.

[21] According to British investigators, Grozev is said to have been shadowed by a group of agents on behalf of Russia in several countries, including Austria, Montenegro and Spain.

The agents, who came from Bulgaria, are also said to have broken into his apartment, stolen one of his computers and spied on his life in Vienna, where he lived for a time.