The space age began with Tsiolkovsky, a school teacher in Tsarist Russia. His theoretical work moved thinking on space flight from the realm of fantasy- Hales story Brick Moon, the works of Jules Verne, etc.- to rigorous mathematical theory. Tsiolkovsky analyzed the requirements of space flight in incredible detail. Before Liquid fuel rockets had even been attempted (the first successful liquid fuel rocket was flown, I believe, in 1928 by the American Robert Goddard) Tsiolkovsky determined that only this type of rocket would have the power too achieve orbital flight. He predicted that the use of staged rockets would allow sizable payloads to be placed in orbit. (He referred to them as rocket trains.) He predicted that eventually mankind would create orbital habitats, and that we would eventually make homes in space for millions of people. He said that "Earth is the cradle of mankind, but one cant live in the cradle forever.
Though Tsiolkovsky was doomed to obscurity, this visionary saw in its entirety the whole future of man in space- not merely the dream of space flight, but how it would be achieved. And he wrote the earliest of his papers before the first heavier than air flight! After the revolution, he was praised by the Soviets as a forward thinker, and a treasure of the Soviet people. But the Soviet government made no real efforts in the field of rocketry.
In the inter-war period, the only place that serious developments in rocketry were happening was Germany. The VfR, or Rocket Society, was the primary vehicle for this development. Its members included all of the most prominent rocket engineers- most of whom would later work at Peenemunde. Mention of this could be indirect, because at the same time, there was a rocket society in the Soviet Union. Small and not very rich in resources or political connections, the (I think it was the All-Russian Society for Rocketry) members of this group began to develop their own line of experimental rockets. Despite the paucity of resources, they were very successful, building bigger and more capable rockets throughout the thirties.
In terms of social context, the changes in the 1930s are very interesting as well. What had started as private volunteer organizations in the late 20s, became government and military projects over the course of the 30s. Almost the entire German VfR became part of Wehrmacht Gen. Dornbergers Rocket program at Peenemunde. Similarly, the Soviet group came under increasing Soviet supervision. (It had always been a state sponsored group- but the higher government officials began to take a greater interest in their activities.)
The work of the soviet rocket experimenters could be compared to the more substantial developments in Germany, because the Soviets followed those developments very closely. During the period of the Nazi-Soviet non-aggression pact, Korolev visited the Germans at Peenemunde. But despite the influence of the Germans, the Soviet program always followed its own style and purpose.
With the coming of the war, the Soviet program was more or less put on hold. Korolev worked with the Tupolev design bureau for most of the war. Its head and namesake had been in the gulags until his services were desperately needed, and was still technically in prison even while designing planes for the war effort.
When the war was won, the Americans and Soviets divided the spoils of the German Rocket program. The Americans got all the high level engineers and plans, as well as about a thousand complete V2 rockets. The Soviets got all the industrial facilities, machine tools, and trained workers. These were all taken back to Russia. The German engineers became the core of the American rocket program. They designed most of the early ICBMs, and several of the civilian rockets later used in the space program (Most notably the Saturn V by Werner von Braun, still the most powerful rocket ever designed.) American born engineers worked with the Germans, and eventually replaced them, but the genesis and style of the American rocket efforts was and remained German.
The Soviets, on the other hand, examined the V2s they had captured, and incorporated some of its technology into their designs. But the thrust of their design efforts remained Soviet in characteristics. (One can see the difference in Soviet and German/American design philosophies by looking at the first ICBMs. The American effort is substantially like the V2- linear, stage upon stage design. The Soviet R7, used later to launch Gagarin, is clearly not a descendent of the V2. Its stage and a half design, with a central core surrounded by drop off stage rockets is both different from the western tradition, and a obvious descendent of the early efforts of the Soviet Rocket society.) They merely used the industrial plant and workers captured in the war to increase their production capacity.
While the Americans would do some research, and build ICBMs, American efforts in the 50s were rather lackluster. Von Braun, in particular, was frustrated at the slow pace of his adopted country. (This man, and his colleagues, had had to hide their engineering drawings from their military and Nazi party superiors because they had always drawn manned capsules on top of the rockets rather than explosive warheads. While he didnt have to hide his desire for space in America, the US government was no more willing to fork out the cash for Buck Rogers Stuff.) Von Braun had done the long series of articles in Colliers, illustrated by Bonestell, explaining how man could get to Mars, before the first satellite had been launched. But no progress was made in this direction.
The Soviets meanwhile, were preparing to force the creation of the space age. Early Soviet atomic warheads were very large, and this had a direct effect on Soviet rocket development. The need for a large military rocket had resulted in the powerful R7 rocket, and it was realized that this rocket could put a satellite into orbit, and - suitably modified - could put a man in orbit.
The development of the modern space race is well documented, but some points can be made: the Soviet efforts in space completely determined the character of American achievements in Space at least through 1980. America had no real space program until after the Sputnik launch in 57. The Vanguard failures were due to the desire for a civilian space efforts despite the fact that proven military rockets were available. Explorer, and later the Mercury program were direct responses to Russian successes.
The entire Lunar program was the result of the fact that a moon landing was the first thing that the Americans would be able to beat the Russians to. Every smaller achievement, it was felt, would be reached first by the Soviets no matter how much effort was expended. So America decided, for almost purely political reasons, to aim for the Moon. As a result, the latter half of the Mercury program, and the Ranger, Surveyor, Gemini and Apollo programs were all the result of one political decision that was made as a result of Soviet successes in Space. (And when the political reasons for the program no longer obtained, the program collapsed. Further, all competing programs, some of which had enormous potential, were sacrificed to reach the Moon. This was known as the Slaughter of the Innocents. Two such occurrences have happened so far in American Space history - the other was during the Shuttle program.)
A second point is the culture surrounding the Soviet space program. Lives were lost due to the push for success: the stupidity and blindness of the Soviet government resulted in hundreds of casualties. The fact that Gagarin was probably not the first man in space. The fact that Korolev was not only denied permission to receive the Nobel prize twice, but even his name was kept secret from the west until after his death. (The Chief Designer.) The lack of modern technology forced difficult, and eventually impossible compromises. The Soviet N1 rocket, designed for moon missions, was unworkable - though its existence was kept completely secret. (The existence of the N1 even controlled the timetable for Apollo missions. When the CIA discovered the N1 on the pad, the timetable for Apollo 8 was, if I remember correctly, moved up over a month.)
The Soviet program kept moving forward on inertia after the successful American moon landing. They focused on long duration space missions, and have acquired the most extensive data on Human tolerance of micro-gravity environments. But the end of the cold war in space resulted in confusion on both sides. Neither side had a political goal, but the field was still too politicized for purely scientific goals to replace them.
Now, in at least one sense, the Russians are leading the world again. They are the first nation to move toward allowing a purely private company to lease and operate a space facility. They were the first nation to allow paying passengers to go into space. (Over NASAs strenuous objections.) Whether this results in more private access to space or not is very uncertain, but its still a first. NASAs sclerotic hold on the American space effort is in noticeable contrast. While these moves are certainly the result of the horrible financial predicament of the former Soviet space program, the fact that the Russians keep trying, no matter how difficult it is, when the vastly richer Americans do proportionally far less is interesting. (Brief sermon, couldnt help myself.)
Russia continues to pursue its space program with all the vigor that its limited budget allows. They are designing a follow on to their venerable soyuz capsule. Hopefully, we will follow their example in privatising space travel. Of course, we have always been following their lead, so perhaps we don't really have a choice.