Leo Express is a private open access operator, which comptes with state railways especially on the busy Praha-Ostrava route, but Leo's trains continue all the way through to Košice in Slovakia. Whereas Regiojet (see below) profiles itself as a budget train operator, Leo wants to be a quality operator. Leo's trains are Swiss made Stadler FLIRTs with quite stylish interiors including a good buffet restaurant.
Picture of a Leo Express FLIRT rushing fast past the Praha-Klánovice station 15.7.2017 by Ilkka Siissalo.

Another one of the Leo Express FLIRT trains, here waiting for its departure time for Košice in Slovakia on the extremely short platform no. 1b of Praha (Prag) main station. The platform is just barely long enough for these luxurious FLIRT trains.
Picture from Praha hlavní nádraží (Prag main station) 15.7.2018 by Ilkka Siissalo.

Another picture of the same Stadler FLIRT train of Leo Express as above. Note how nicely its windows act as mirrors.
Picture from Praha hlavní nádraží (Prag main station) 15.7.2018 by Ilkka Siissalo.

One of the first real state railways competitors in Czech republic was Regiojet. The company was founded in 2009. First they used old former state railways Škoda locomotives and all kinds of old coaches they could find, but since the beginning Regiojet has expanded a lot. They have bought a large fleet of InterCity coaches from Austrian ÖBB, Swiss SBB and Belgian SNMB and modernised them. Most of Regiojet's trains are today led by modern Siemens Vectron locomotives capable of running under multiple electric systems. For example this Vectron, no. 193.206 is in German register and owned by the company European Locomotive Leasing ELL.
Picture from Brno station 14.7.2018 by Ilkka Siissalo.

Another view of the same Regiojet Vectron. The company profiles itself as a cheaper alternative to the state railways and it is especially favored by student age young people.
Picture from Brno station 14.7.2018 by Ilkka Siissalo.

There are still fairly few and small open access private cargo operators in Czech republic, but Advanced World Transport AWT is one of them. The macine is an old Czechoslovakian state railways class T486.2, now class 742.500 of which 41 were made 1983-1986. It is a 883 kW diesel intended for "midrange to heavy" shunting and main line operation, with a top speed of 90 km/h. Of these only 41 locomotives were made, but the precursor model, which has a much taller shorter front section was built in over 450 copies and has also been thoroughly rebuilt now to yield totally new locomotives of the class CDC 742.7. The variant with a taller short front section is fairly common in CZ and SK, but this one is not.
Picture from Usti nad Labem station 15.7.2018 by Ilkka Siissalo.

Detail picture of the same class 742.5xx locomotive as above.
Picture from Usti nad Labem station 15.7.2018 by Ilkka Siissalo.

Still the same locomotive, but seen from the other side. It's easy to see that the basic design is copied from USA from their 1930s designs via those few machines that USA delivered to the USSR still during WWII. This machine still looks outside as it used to be, but according to the stickers on its sides it has already been modernised by the company CZ Loko and has new Caterpillar engines. CZ Loko has rebuilt many more old Czech engines and is reselling them as cheaper but new locomotives for example to the Baltic states, Finland and Russia.
Picture from Usti nad Labem station 15.7.2018 by Ilkka Siissalo.

Some of German state railways DB's cargo trains come all the way to Czech Republic, where they are typically driven by CZ's train drivers. This is a view from the driver's cab of a German Br 189 EuroSprinter locomotive of DB. The locomotive was leading a long container train.
Picture from Melnik in January 2017 by Michal Makalouš.

Two long coal trains with German multiple electric system Siemens EuroSprinter Br189 locomotives at the Czech station of Děčín. The one on the left was just standing idle. But the train on the right is the train 45300 Děčín - Halle. The train was 485 m long and like 1100 tons heavy.
Picture from Děčín 9.12.2019 by Michal Makalouš, who was the driver of the train who drove it to Dresden.