The largest and most powerful empire in world history is the United States of America.
You may be thinking of empires as largely defined by territory. This is convenient for historians (and history teachers) as lines on a map over time are an easy way to explain the rise and fall of great powers. However, this is only one way to describe a type of empire.
However, America as an empire is not strictly defined by its borders. Yes, there was a lot of conquering and wiping out of indigenous populations, and yes, there were quite a few military expeditions that granted the U.S. control over a sovereign territory (the Philippines come to mind), but the true power of the American empire is economic.
Why send the Marines when you can use the World Bank and the International Monetary Fund to force other countries into accepting your economic dominance?
The typical modus operandi for American economic dominance works like this: pressure the authorities in another country to accept trade agreements which "open up" and "deregulate" foreign markets, in exchange for access to the wealthy American market for exports and cheap American credit lines. What this usually means is remove protections and subsidies for domestic corporations and force them to compete on even footing with the vastly superior resources of American corporations and banks. Before long, the local economy is gutted and dependent on America both for imports (for domestic goods that cannot be produced locally) and exports (as a way to make money at all).
As a result, one may find no other solution than to accept the terms and succumb to the host's economic empire. Even if no shots have been fired and no borders redrawn, the empire now has the smaller state firmly in their grasp.
And if all else fails, get the CIA to overthrow democratically elected governments formed on the basis of getting a better deal for their labor.
Exception to my header: other nations are figuring this out.
Just because the U.S. is the world's largest and most powerful economic empire doesn't mean the position is eternal, nor is it exclusive. Other nations, in particular China and Russia, have been using the same tactics to expand their economic clout without military action (if you forget about Crimea).
Something to consider as a parting thought: if every nation in Europe suddenly boycotted Russian oil and natural gas, that would be as much a blow to the Russian economy and their basis of power as military conquest in oil-rich Siberia. Some 50% of the Russian government's budget is dependent on oil exports.