I've been polishing this definition for years.

"Any political entity that is designated, whether by self or others, as aspiring to hegemony."

I word it this way because we have to find a way to incorporate entities such as the Athenian Empire (which didn't call itself that) or the Chinese Empire (that word has a different connotation in the language) or the Korean Empire (purely aspirational) to a mafia empire (not exactly a state).

Please adopt my buzz phrase.

My definition is a little different from /u/bitparity's because I see empire from basically the other end: when I study nationalism, empires are one of the things (along with city states, principalities, etc.) that come before nation-states. For me, the defining thing about an Empire is that it's rule over culturally heterogeneous peoples. In many language, the word for emperor is either a direct borrowing from Latin or translates as "king of kings". The King rules over a people, an emperor rules over many kings is the implication. The term Padishah, the most common term for the Ottoman Sultan, is a borrowing from Persian (as many Ottoman terms are) where pād means "master" and shāh means king. The Persians tended to prefer the straight up Shāhanshāh. The term is an ancient and common one in the nearest, and spread at least far as Ethiopia.

I don't know what bit-party uses it for, with once independent states becoming subject empires, but on my end, the transition from Empires to Nation-States (and, occasionally, State-Nations like the U.S. and India) is one of the most important transitions. Empire is big right now.

What I found immensely interesting about this discussion and the contributions of /u/bitparty and /u/yodatsracist below is how language contributes to it. In my native language of German, when we refer to "Empire" (untranslated) it is almost always a reference to a certain technique of power, meaning it refers to to what Hobsbawm terms the "Age of Empire" in the 19th century and the establishment of colonial empires by the British, French etc. It is specifically used to denote this kind of relationship between rulers and ruled as well as the implied exploitation on a political and economic level.

At the same time the German term "Reich" would be the broader term, e.g. used with the Holy Roman Empire (the Heiliges Römisches Reich), which no one here would call an "Empire". In terms of translating this to English, the funny thing to me is that the Holy Roman Empire becomes an empire in English while the Third Reich, which employed the techniques of power colonial empires used since the 19th century on other Europeans, remains a Reich despite being very empire like.

From an earlier answer

"Empire" is a term is incredibly slippery term for historians to define. Empires are often very complex entities and trying to extrapolate some general features means there is a loss of nuance. For example, Charles Tilly came up with a serviceable definition for empire:

An empire is a large composite polity linked to a central power by indirect rule. The central power exercises some military and fiscal control in each major segment of its imperial domain, but tolerates two major elements of indirect rule: (1) retention or establishment of particular, distinct compacts for the government of each segment; and (2) exercise of power through intermediaries who enjoy considerable autonomy within their own domains in return for compliance, tribute, and military collaboration with the center.

Tilly's definition is quite flexible, but also deliberately quite vague and can be stretched too far. For example, one can use Tilly's definition to label the US's immediate postwar position in Western Europe an empire with economic agreements like Bretton Woods, institutions like NATO, and foreign aid like the Marshall Plan as a instruments of an American imperium. But nations like France, West Germany and the UK retained a significant amount of autonomy and national sovereignty and when looking at the State Department archives there is considerable consternation over their allies' independence. This is one problem with labeling state entities as empires haphazardly, once you stretch these conceptualizations too far, the term itself becomes distorted and loses its original meaning.

If you're so inclined, the German Historical Institute London held a plenary forum, Empires and Colonies with some leading imperial and colonial scholars that discusses the various historical approaches to this subject that goes into some of the weeds of this very topic.

I tend to agree with /u/bitparity on his definition, maybe because of my field. The main characteristic of the HRE in the context of western medieval politics is that it had universal aspirations, upon which it clashed with the church, which itself is referred to by some medievalists (including me) as something of an imperial entity. Interestingly, I think the medieval vision of the Empire may be the fundamental core of western European political thought: everything from republic to modern states, and perhaps even more interestingly, it seems to be highly devoid of national connotations.

Why was Queen Victoria just Queen of England, but Empress of India?