In the mid-1500s the Russians finally rid themselves of the Tatars. Then, with the fall of the Byzantium Empire in 1453, the Russians claimed themselves as the legitimate successor to the thrown and solidified this claim by Ivan the Great's marriage to the niece of the last Byzantium Emperor. The remnants of this are still visible today as Russia's coat of arms, the double-headed eagle was taken from Byzantium. After Ivan the Great came Ivan the Terrible, who was the first to use the title "Tsar" from the word "Caesar," again claiming the Byzantium thrown, which was established from the historic Roman Empire.
The late 1500s saw a rapidly expanding Russian Empire as they pushed east into Siberia. This push also began the rule of the Russians over multiple minorities, particularly the Tatars and small Asiatic groups who were scattered everywhere throughout Siberia and just west of the Ural Mountains. This strong rule was short lived at first as the Tatars in the south, Poles in the west, and Swedes in the north began to encroach on Russia, getting so far as briefly taking Moscow in the early 1600s. However the Russians quickly retaliated and in the late 1600s took much of present-day Ukraine as those people rebelled against Polish rule and were swallowed up by Russia. Meanwhile, there was little resistance or organization among Russia's neighbors to the east so their push towards the Pacific Ocean continued; in 1648 the Russians reached Alaska via the Bering Strait.
The 1700s saw more prosperous efforts by the Russians (particularly under the rules of Peter the Great and Catherine the Great) as they defeated the Swedes, founded St. Petersburg as a large Baltic Sea port city, and defeated the Poles and took about a third of their former country. The 1800s was much of the same as Russia continued to expand and was famed throughout Europe for defeating Napoleon's forces.
In 1905 revolution broke out in Russia, then the country was thrust into World War I, but faced another revolution in 1917 before war's end. This revolution established the Soviet Union in 1922, which grew over time, but Russia remained the dominant republic in the union throughout its history.