Since the Soviet Union and the United States were competeing in everything, including technology, the Soviet Union too had their own radar. Like in North America, they drew on different types of radar.
They had their own early warning radars, located at Minsk, Riga, Kiev, Pechora, Yary, and Urals, as well as approximately 8 phased array radars on the periphery. They also had air surveillance radars (about 7,000 located in 1,200 different places).
The Soviets also had SAMs (Surface-to-Air Missiles), notably, the SAM-2 “GUIDELINE” which was controlled by radar. Many within NATO were afraid of these missiles because they could easily reach a supersonic aircraft, even when flying at a high altitude. During the Vietnam War they gave these missiles, as well as their SAM-3 to some of their allies which hurt the Americans.
Soviet planes also drew on radar. Their more modern planes, like the Fencer, Backfire, and Blackjack had good radar and combined this with the ability to fly under the radar horizon.
The United States did not always realize how much radar the Soviets had, or how capable it was. This allowed the Soviets to surprise the Americans when they used it to shoot down a U-2 plane flying in Soviet airspace.
There were instances when they were more advanced in the radar they were using. In 1974, for example, the Soviet Union had the only antiballistic missile defense system which they brought together with radar and interceptors.