Short answers, pulled from the story.
A sphere of influence is a spatial region where one state holds cultural, economic, military, or political exclusivity. Unlike formal alliances that require treaty obligations, spheres often rely on soft power to maintain control.
President James Monroe later formalized this doctrine to remove European powers from the Americas after Alexander Hamilton wrote about establishing such a sphere across North America in the Federalist Papers. This historical policy continues to shape modern diplomatic relations in the Western Hemisphere today.
In early 1895 France laid claim to a sphere in Southwest China while Germany declared its intent to seize territory by December 1897. Kaiser Wilhelm II precipitated a scramble to demarcate zones of influence across Chinese land involving Russia, Japan, Britain, and Italy.
A secret protocol attached to the Molotov-Ribbentrop Pact of 1939 divided Northern and Eastern Europe into Nazi and Soviet spheres assigning Finland Estonia and Latvia to the Soviet sphere. Lithuania initially fell under German influence before a second secret protocol in September 1939 assigned it to the USSR.
The Eastern Bloc fell apart effectively ending the Soviet sphere of influence when the Soviet Union ceased to exist in 1991. This geopolitical split defined global politics for over four decades from 1947 until the dissolution of the superpower state.
Boris Yeltsin issued a statement dated September 1994 portraying Commonwealth of Independent States countries as part of Russia's sphere. Russian president Dmitri Medvedev stated five principles of foreign policy on the 31st of August 2008 claiming a privileged sphere comprising border regions.