Hey there. The history behind this region is extremely old, complicated, and full of information that clashes together. A fair warning though, I am ethnic Armenian but I will do my best to provide a well-rounded approach. I won’t be giving a full historical perspective to the region, I’ll focus on the relevant parts of the last 100 years. However, it is generally agreed by the overwhelming majority of historians that Armenians are the indigenous populations of these lands and have lived here continuously for thousands of years. If a deeper dive into the history is requested then I would be glad to offer my insights.

What is known as "Karabakh" is a fairly broad region and it was not known by this name until much later in its history. The region in question is a large part of the dark red area known as “Artsakh” in Armenian or “Mountainous/Nagorno Karabakh” or sometimes it might be called “Upper Karabakh” and the boundary of the self-declared Republic of Artsakh following the ceasefire of 1994 is the dashed lines. To start with the important bits, following the collapse of the Russian Empire the Transcaucasian republics of Georgia, Armenia and Azerbaijan formed a joint republic then declared independence from the republic and immediately went to war which was littered with tremendous crimes, massacres, pogroms, deportations, etc. The status of the region was disputed both before and after the Sovietization of the region (Sovietization occurred in 1920-1921 and Azerbaijan was the first to Sovietize). Its disputed status was put on hold and temporarily placed within the jurisdiction of Soviet Azerbaijan and the Kavburo (based out of Baku) until it can be resolved following Armenia’s Sovietization with Soviet Azerbaijan suggesting that it be placed under Armenian control. When Armenia’s Sovietization came, the region was placed into the borders of the Azerbaijan SSR and granted autonomy as the Nagorno-Karabakh Autonomous Oblast - NKAO for short with an overwhelmingly Armenian population. The story behind why Nagorno-Karabakh was placed inside Azerbaijan with autonomy is a pretty long one and I will elaborate further if requested.

In 1923 the NKAO was officially established within the borders of Azerbaijan SSR. Since then, the government of the Azerbaijan SSR pursued a policy of socio-economic discrimination and political repression that made life difficult for the Armenians as well as carrying out a policy of demographic change that was intended to reduce the number of Armenians. Former President of the independent Republic of Azerbaijan Heydar Aliyev (who served as the First Secretary of the Communist Party of Azerbaijan between 1969-1982 and as First Deputy Premier of the USSR between 1982-1987) stated that he had carried out systematic attempts at demographic change in the region “to increase the number of Azerbaijanis and decrease the number of Armenians." The Armenian population of the NKAO went from ~90% in 1926 to ~75% in the 1980s according to the USSR population census, some sources put the number in the 1920s closer to 95% but I’d rather just go with official statistics. Throughout the next 80 years of the USSR, Armenian-led movements to bring the NKAO within Armenian jurisdiction arose. It came as early as 1946-1948 when ethnic Armenian politicians such as Grigor Harutyunyan petitioned USSR leadership to unite NKAO with Armenia and most notably in the 1960s when Anton Kochinyan did the same. However, the situation in the 1960s was already different because it was accompanied by massive protests that were not related to the NKAO issue but rather demanded that USSR leadership officially recognize the Armenian Genocide. Other grievances were highlighted mainly in the situation with NKAO but also the treatment of Armenians in other parts of Azerbaijan SSR, most importantly in the Nakhichevan ASSR. Nakhichevan is another region that was in dispute, in the early 20th century its Armenian population was nearly 40% and by the 1980s it was almost non-existent. I bring up Nakhichevan because this region and the drastic disappearance of the Armenian population from here was in the dwelling on the minds of Armenians and leaders of what became known as the “Artsakh Movement.”

There were not massive demonstrations such as this until the 1980s, if we were to look at the same interview with Heydar Aliyev I mentioned above we can also see that he claims to have played a hand in preventing the movement from picking up but after his resignation in 1987, he was unable to influence it anymore. In reality, it was unlikely that he willingly resigned but rather he was removed from office. The timing also coincided with Gorbachev’s perestroika and glasnost reforms. From November 1987 to February 1988, three separate delegations from the NKAO visited Moscow to discuss unification. In 1987 alone: thousands of letters were sent to Moscow by Armenians and many petitions were also sent, including one petition which had over 80,0000 signatures including signatures from 40 deputies of NKAO. Armenian demands were turned down by Soviet Authorities and this caused massive (yet peaceful) Armenian demonstrations to erupt across Azerbaijan and Armenia. The Azerbaijani reaction was extremely violent and culminated in massive anti-Armenian pogroms starting in February of 1988 (notably in Sumgait and Kirovabad/Ganja but also in smaller towns such as Sushi/Shusha) that left hundreds of Armenian dead, thousands wounded, and hundreds of thousands of Armenian refugees overnight. The pogroms were often attributed to the Azerbaijani reactions to the movement to unify Artsakh with Armenia and the second was the Azerbaijani government spreading rumors about attacks against Azeris in Armenia (The claims of anti-Azeri events occurring in Armenia are generally believed to be false, there was no media coverage of them nor was there any official documentation of them occurring). Following the pogroms, Soviet authorities began the transfer of populations from the two SSRs and removed NKAO from the administrative jurisdiction of AzSSR, creating a special commission to administer the region (note: the constitutional status of the region was not modified).

In late 1989 the Armenian SSR and the NKAO Committee passed a resolution regarding the official unification of NKAO with Armenia and on 9 January 1990 the Armenian SSR discussed establishing an official budget for the NKAO, both actions were seen as major provocations. The news was met with another set of pogroms against the Armenian populations in January of 1990, specifically in the town of Baku. The majority of the Armenian residents of Baku (Baku had a long-established Armenian community that historically made up almost 30% of the city’s population, but in the 1980s it was around 17% or 170,000 people according to Soviet Census) had already left, the remaining Armenian population was around 40,000 with the majority being women or pensioners. On 3 April 1990, the USSR passed the “Law on Secession” which granted Soviet Republics AND autonomous regions the right to self-determination through a referendum. In March 1991, the Armenian SSR decided to hold an independence vote scheduled for 21 September 1991. This was viewed as a threat by Gorbachev who attempted to revitalize the USSR and Soviets authorities carried out “Operation Ring” targeting ethnic Armenians mostly in the Shahumyan region but also in other parts of Armenia/NKAO that led to ~50 deaths and thousands of Armenians being deported. On 2 September 1991, the Nagorno-Karabakh council and the Shahumyan regional council declared their independence from the USSR within the borders of the NKAO and Shahumyan region. The Azerbaijan SSR immediately began shelling and rocket attacks on the NKR’s capital of Stepanakert as well as other locations. On 26 November 1991, Azerbaijan formally dissolved the NKAO and renamed Stepanakert to Khankendi (The important thing to note here is that NKR [now the Artsakh Republic] had declared independence and attained their independence before the dissolution of the USSR meaning that legally speaking their independence should be recognized the same way the independence of other post-USSR countries is recognized). By the start of 1992, full-scale war had begun and was paused under a ceasefire in 1994 until recently.

/u/avedji has previously answered Why do Azerbaijan and Armenia each have enclave territories inside each other?

I look forward to more well-written, well-sourced answers on this topic. Since the Powers That Be have anointed this one the Great Question version, maybe it will get more traffic.