Unlike the short-range rockets which are all solid fueled, making a solid-fuel long range rocket is very challenging. The main technical problem is that the fuel block which is very large can develop a crack under mechanical and thermal stress. The flame will immediately spread into the crack, and the whole thing will explode.
The second difficult problem is how to cool down the nozzle. In the liquid-propelled rockets it is cooled by the fuel. In short range rockets the engine works very short time and no cooling is needed.
For the history of German rockets, and in general for the early rocket history (till the late 40-s) there is an excellent classical book:
Willey Ley, Rockets, Missiles and Space travel. (Strongly recommended).
The Russian side of the story is described in the books of Chertok (4 volumes in Russian).
He mentions a breakthrough in solid fuel development made in Caltech in the early 50-s, the thing they just could not match in Soviet Union.
All early Soviet long range rockets, even those launched from submarines were liquid fueled. Because the Soviets could not develop solid fuel technology needed for large enough engines. (Just imagine a liquid fuel rocket launched from a submarine!!) Earlier models could not be kept fueled inside in a submarine, so they had to undergo a long and extremely dangerous fueling procedure immediately before launch. If the launch was aborted after the fueling began, the rocket had to be just damped overboard:-)
This shows that the problem is highly non-trivial.
Roughly speaking the fuel block must be mechanically strong and elastic.
And the nozzle has to withstand enormous temperature for relatively long time.
I am afraid that a complete scientific story of (long range, intercontinental) solid fuel rockets is not written yet: the Russians used liquid fuel rockets until recently, and maybe still using some of them.
EDIT. 1. I should mention that liquid fuel rockets have also some advantages: you can regulate the engine power during the flight. It is much more difficult with solid fuel.
- Actually all three currently operational Russian submarine based ICBM use
liquid fuel, one of them has liquid and solid on various stages. See
Wikipedia article "Submarine-launched ballistic missile".