[2] Its first missions were to restore public order in areas where Serbs participating in the Log Revolution were trying to wrest control from the authorities; to take control of the barracks and confiscate weapons of the Yugoslav People's Army, whose authority in Croatia was rescinded by the country's government after it sided with the Log Revolution; and to train units which would later be organised into the Croatian Armed Forces.

[6] Members of Lučko ATU's chain of command, including General Mladen Markač, were tried by the International Criminal Tribunal for the former Yugoslavia (ICTY) for alleged war crimes committed during Operation Storm.

Applicants, who must already be police officers with at least four years of experience, are required to pass a demanding battery of tests, and only around 5% are admitted to a 12-month training regimen necessary to join the unit.

[10][11] Lučko ATU is a member of the ATLAS Network of European police tactical units, and also trains with American SWAT teams.

[13][14][15] He wore his Croatian special police uniform at press conferences,[14] leading to his mixed martial arts nickname "Cro Cop".

[13][15] Seven generals of the Croatian Army were previously members: Slavko Butorac, Miljenko Filipović, Mladen Markač, Mirko Norac, Ante Roso, Željko Sačić and Stanko Sopta.