It is difficult to answer the question without it delving into current politics because even history is being used to politicize the events.

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Crimea was conquered by the Russian Empire in 1783 following the independence of the Crimean Khanate following the Treaty of Küçük Kaynarca in 1774, signed between the Ottoman and the Russian Empires. Following this the peninsula was part of the "New Russia" initiative set by originally by Catherine the Great and her successor Paul. Following that it was formally part of the Russian Empire and was part of a Governorate. The Crimean Peninsula was fundamental in the wars the Russian Empire fought, its height of importance being the Crimean War in 1853-1856. There was lasting wars and the Siege of Sevastopol.

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Following the Russian Revolutions and the Russian Civil War the Crimean Peninsula was formally part of the Russian Soviet Federative Socialist Republic. Without going into deep detail on the complicated and confusing nature of the Soviet Union bureaucracy, a Socialist Republic was nominally an independent nation in Union with the other Republics in the Soviet Union. In practicality, it was subservient still to the Communist Party of the Soviet Union (CPSU). However, this detail is important because while Crimea was part of the RSFSR in 1954 it was transferred from the RSFSR to the Ukrainian Soviet Socialist Republic. This decision was not done via referendum or any decision by the population of the people on the peninsula. In an article in Pravda the reason given was:

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Taking into account the integral character of the economy, the territorial proximity and the close economic and cultural ties between the Crimea Province and the Ukrainian SSR, the Presidium of the USSR Supreme Soviet decrees:

To approve the joint presentation of the Presidium of the Russian SFSR Supreme Soviet and the Presidium of the Ukrainian SSR Supreme Soviet on the transfer of the Crimea Province from the Russian SFSR to the Ukrainian SSR.

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The move was seen post-decision as a symbolic gesture to celebrate the 300th anniversary of Ukraine being part of Russia. Nikita Khrushchev, the Soviet General/First Secretary had a great affinity towards Ukraine, and the decision was his to make. His son claimed it was purely administrative saying it likely had to do with a dam on the Dnieper River. The point being, that at the time in 1959 Ethnic Russians totaled 71.4% of the population in Crimea, with Ethnic Ukrainians only totaling 22.3%.

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By the fall of the Soviet Union and the subsequent dissolution of the separate Republics which ended up becoming successor states, Crimea belonged, on paper, to the country of Ukraine. At the time, Ethnic Russians were at 67% and Ethnic Ukrainians were at 25.8%. The Crimeans voted to become autonomous in 1991. Thus Crimea became the Autonomous Republic of Crimea, its parliament in 1992 voted for further autonomy and scheduled a referendum for complete autonomy in August, 1992. However, it was quickly brought to heel by Kiev and the referendum was never voted for. The Crimean Constitution which was also voted by the same parliament in 1992 on was also null and voided by Kiev in 1995, as Ukraine asserted its dominion over the Republic in its borders.

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In 1997 (the latest I can provide information on based on the rules of the Subreddit) a Treaty was signed between Russia and Ukraine called the Russian-Ukrainian Friendship Treaty which specified, in regards to Crimea, the inviolability of each others borders and established that the current borders were de facto correct and without grievance. It was ratified by both countries and was set to auto-renew every ten years unless the other declared they wanted out.

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I think we cannot hold that one side, either Ukraine or Russia "owns" the Crimea or have more "claim" to Crimea. Crimea should belong to those that live there and seeing that Khrushchev tossed it to Ukraine for a good will gesture without consultation, and then when there was a referendum on independence set that got curtailed by Ukraine. Often this is the case in European politics, where ideology or Empire trumps self-determination. Crimea should belong to the Crimeans and if they want to be part of Ukraine, great, Russia? Thats fine too. By themselves? All the best.