In terms of the position of the United States, the policy was one of "containment," in which the Us tried to stop the spread of communism through proxy wars and covert operations. For the USSR, they tried to take over as much new territory as possible.
Many countries have set out their own explorers. Columbus’s discovery of the West Indies had started the quest for the New World. Many explorers were able to conquer new lands as they set out for the New World. Jacques Cartier was able to discover Canada while the Spaniards were able to conquer South America.