1. Both the USSR and the USA spent huge amounts of money to conduct research into weapons. 

2. They build arsenals of devastating nuclear arms and missiles. 

3. They could strike across the continents. 

4. They had enough nuclear arms to destroy the entire earth many times over. 

5. Gradually their allies like Britain, France and China too built nuclear arsenals.

6. People of all countries lived in constant fear of war. 

7. Many times war looked imminent but got defused somehow through diplomacy.

8. There were many flash points which made everyone believe of the triggering off another world war. 

9. But when both ultimately realised the implication of a nuclear war both started working for arms control and many arms control treaties were signed like CTBT, NPT, etc. 

10. Both decided to follow the logic of deterrence which meant that both have the capacity to attack and cause so much destruction to threaten the existence of the other. But neither is willing to start the war due to the amount of destruction.