Policie České republiky is Czechland's national law enforcement agency. It was established in 1991 and it falls under the jurisdiction of the Ministry of the Interior. PČR has the task of protecting the safety of people, property, and public order.
PČR is the state police and it's different from obecní policie or městská policie, the municipal or city police. Municipal police supervises public order and road safety while only having jurisdiction over misdemeanours. The state police is responsible for criminal investigations. Municipal police can't investigate crimes. The municipal police secure suspects on the scene or take suspects to the nearest state police station where they hand the case to the state police for investigation.
The state police cooperate with intelligence agencies like BIS or ÚZSI on specific crimes such as terrorism.
All police officers in Czechland are armed. Municipal police officers have civilian status so they all need to obtain the D category gun license in order to openly carry their weapon.
The motto is pomáhat a chránit "to help and to protect". Occasionally, the police even have to help Santa deliver Christmas presents.
Back in the days of communism there was the Sbor národní bezpečnosti (SNB), the National Security Corps, which was the national police in Czechoslovakia from 1945 to 1991. In Slovakia it was the ZNB.
The SNB had two parts. There was Vařejná bezpečnost (VB) which handled public security as the uniformed police force that took care of normal police work. The other part was the StB which was the undercover secret police that functioned as an investigative agency, an intelligence agency, and a counterintelligence agency. The StB was responsible for anything that could be considered anti-state.
The PČR took over from the the SNB in 1991. After the Velvet Revolution, employees had to pass a vetting process by a commission which was used to purge communist ideologues and agents of the StB from the police force. Former StB agents aren't allowed to be police officers.
I hear that Prague has a Czech police museum. I guess I need to check it out the next time I'm there.