The Klingon Empire is located "east" of the Federation, in the Beta Quadrant. It is "north" of the Romulan Star Empire, and occupies an area roughly a third of the size of the Federation and is shown on the map above in white. There was once a Neutral Zone between the Klingon Empire and the Federation established by the Organians; it was abolished by the Khitomer Accords in 2293.
The Klingon Empire is centered on the world of Qo'noS, frequently referred to merely as the "Klingon Homeworld". It was founded some fifteen hundred years ago by Kahless the Unforgettable, who vanquished the tyrant emperor Molor and seized the empire himself, uniting all the Klingon peoples. The Empire then began a program of conquest and expansion that continues to this day.
The Klingon Empire is governed by the Klingon High Council, which meets in the Great Hall of the First City of Qo'noS. The High Council is composed of some two dozen individuals from prominent families, lead by a Council Leader. The Council Leader serves for life, and is chosen according to a Rite of Succession presided over by an Arbiter of Succession. The Arbiter verifies that the previous Council Leader is dead, and selects challengers from among members of the High Council. The challengers then fight to the death; the victor becomes High Council leader. Despite the title, the Klingon Empire is not truly an empire, as there has not been a successor to Kahless in centuries. The Empire maintains a military called the Klingon Defense Force. It is separate from Starfleet, but often operates in concert with it.
The Klingon Empire used to maintain colonies as a source of resources and labor - particularly for those tasks that were "beneath the dignity of a warrior". These colonies were better off than Romulan ones, but not by much. Klingon treatment of their colonies changed somewhat as a result of the Organian Treaty, which awarded colonies to whichever power developed them better. As a matter of necessity, the Empire gradually learned methods of wiser management to compete effectively with the Federation in the Organian Neutral Zone, and the recent union with the Federation has accentuated these trends.
First contact between the Federation and Klingon Empire took place in 2218, and resulted in nearly a century of hostilities. Both powers were at the brink of open war in 2267, when an advanced alien race imposed the Organian Peace Treaty. This ended the threat of open war, although a cold war continued for some time. The Empire allied with the Romulans against the Federation in 2268, gaining cloaking technology in the process, although this alliance did not last long. The Federation/ Klingon cold war ended in 2293 when the moon Qo'noS's moon Praxis exploded, leaving the Klingon Empire facing an ecological catastrophe if it did not accept aid from the more technologically-advanced Federation. Federation bravery and sacrifice at the Norenda III incident in 2344 won the grudging respect of the Klingon people, and paved the way for a greater union. Proof of this was the selection of a non-Klingon Arbiter of Succession in 2367. A brief civil war in 2368 between the followers of Gowron and those of Duras resulted in Gowron's firmer grasp on the Council Leadership.
Two recent events have shaken Klingon society. The first was the messianic return of Kahless the Unforgettable in 2369. This was proven to be a fraud perpetrated by the clerics of Boreth; they had created a clone from cells of Kahless and taught it to behave like Kahless. Nevertheless, this "Living Kahless" won great support and popularity among the Klingon people, and Council Leader Gowron was forced into awarding him the position of ceremonial Emperor, making the Klingon Empire truly an empire for the first time in centuries. Possibly at the instigation of the "Living Kahless", the Klingon Empire went to war with the Cardassian Union in 2372 on the pretext of Changeling infiltration. The Empire seized and is currently holding on to several Cardassian colonies. The Khitomer Accords between the Federation and the Empire have broken down, and a new era of cold war has begun.
Klingons are warriors by nature and habit, and as such are not great merchants. Nevertheless, they do engage in trade; their unit of currency is the kellikam. Socially, technologically, and economically, they are behind both the Federation and the Romulans.