The Venera and Vega programs launched 18 different craft towards Venus, and there are some other Soviet Venus missions I haven't accounted for here I think. I believe that the Soviet Union is still the only nation to have ever successfully landed craft onto the Venusian surface, although none of them lasted much more than a couple of hours.
The United States hasn't put anywhere near as much resources into exploring Venus, the highest profile missions are some of the Mariner missions and the Magellan mission. A lot of the US visits were also en route to other planets.
Considering how comically difficult it is to explore Venus even now, let alone with technology from the 60s and 70s, why did the Soviets decide to devote so much time and resources to Venus? Other places, most notably Mars, have their own problems but seem like they would be much more reasonable as a focus for a country like the Soviet Union, at least since successful landers don't get destroyed by the nightmarish conditions on Mars after less than an Earth day. Was there a sense that Venus was 'ours' for the Soviets, since they had put so much effort into exploring it? Even now the Russians seem to feel a sense of ownership towards Venus in particular.
The early Soviet planetary program devoted equal attention to Mars and Venus; they built a sequence of nearly-identical probes that were sent to both worlds. Project "MV" started in 1959 intending to send "1V" vehicles to impact Venus in 1960 and "1M" to fly by Mars in 1961. Two copies of the Mars version were launched, both failed to reach orbit. Two copies of the Venus version were also launched, and one made it out of Earth orbit but its stabilization system failed during cruise. It passed quite close to Venus, and likely made planned observations, but was unable to communicate them to Earth. This mission would be called "Venera 1" since it made it to Venus, more or less. "Mars 1" would have to wait.
To be clear, 1 out of 4 isn't bad for the Early Space Age. Success rates of both launchers and payloads were low.
By the time the next Mars window rolled around, they had second generations MV vehicles ready to go. Three tries to send a 2MV to Venus failed, but one of the three Mars attempts actually made it to Mars cruise, earning the name "Mars 1". It failed on the way there.
The 3MV generation would fare better. This time they sent 6 variants of 3MV to Venus, of which two were successful enough for names. Venera 3 did a fly by and took atmospheric data, and Venera 4 managed a "lander". The lander was immediately destroyed, as it was built assuming a much more reasonable Venus; data from an earlier successful American Mariner flyby had basically figured out what the atmosphere was like, but around 1964 when the project was designed, the Soviets, at least, still harbored hopes that the temperature readings from Venus indicated a hot thermosphere but didn't preclude a habitable lower atmosphere.
Three 3MV were sent to Mars; the first failed to launch, the second failed early in cruise, and the third was so delayed that it missed the Mars window but was sent by the Moon on the way to the orbit of Mars.
The Soviets would continue to send regular missions to Mars for the next several synods with marginal success. Mars 2 and 3 would manage to orbit Mars for decent missions. Mars 4 missed the planet for a distant flyby, Mars 5 entered orbit but failed after 10 days. Mars 6 was a lander and failed during Mars descent. Mars 7 missed Mars entirely. After several synods of essentially failure, they let the Mars program lapse without designing a new generation.
Regular missions to Venus met with much more success, and continued for a decade longer. I don't know of any documentation stating as such, but I expect it continued when Mars didn't because it worked.
Venus was in several ways a more suitable target for the Soviet program, which had big launchers and tended towards robust relatively simple designs and iterative learning and design. The thick atmosphere of Venus makes landing on the planet rather trivial if you can survive the heat and pressure, which is of course the main challenge. (In fact, the atmosphere is so thick you don't even need a parachute to land softly! Terminal velocity on Venus is something like 15-20mph, slightly faster than a parachute on Earth.) A big simple robust lander was right in the Soviet wheelhouse, especially when they were able to launch regularly.
Mars on the other hand is a beast to land on. The cruise is long, the launch windows rare and short, and the atmosphere is thin enough it doesn't slow you down much and requires propulsive landing, but thick enough you have to survive a hot entry. This better suited the NASA approach with smaller, more expensive launchers, delicate computerized systems, and extensive pre-mission design, analysis, and quality control.