Historically, which empire was most associated with having control of the baltic states?

The Russian Empire, then Soviet Union

Explanation:

The current states of Estonia, Latvia and Lithuania were states that in the medieval age came to change from the hands of the German to the ever increasing presences of a vast Russian Empire. Wars of conquest between them made important changes in the balance of power in the region. This means they were under German and Russian influence at changing times Prior to World War, these states were controlled by Russia, then after signing the retreat this independent countries laying in the East of the Baltic Sea, came to be independent from Russia.

Provisional goverments often took place, and wars of independence were fought against Russia. Estonia in 1917 became then ocuppied by German Reich, but still as Soviets signed an armistice they lost control of these Baltic states in WW1 Aftermath. This changed again as Soviet Union was victorious and retook control of the Baltic states laying to the East of the Baltic Sea, then Soviet Republics became for Latvia Lithuania and Estonia.

The city of Kaliningrad remains a city to Russia that still exters pression to regain its former power in the region.

Answer: the Soviet empire

The Baltic states are composed of countries in the European Union such as Estonia, Latvia, and Lithuania. These 3 states border the Baltic Sea. Historically, the Soviet Empire was the one most associated with having control of these three Baltic states.