"Where should Crimea belong" is a political question. It's one which historians can't answer; it's also not allowed on this sub, so I have removed this question.

You are welcome to repost this question if you reformulate it to make it solely about the history of Crimea. For instance "What countries has Crimea belonged to in the last couple of centuries" or "How did Crimea become a part of Ukraine" or "What is the relation between Tatars and Crimea" or something like that.

Don't ask for anything which has happened in the last 20 years though, as that too is not allowed in this sub.

Questions like this are impossible to answer.

Let's not forget that crimea was an independent kingdom from the 15th to the 18th centuries. You can argue that Crimea should be an independent country! Around the same time, portions of Crimea were also ruled by the Republic of Genova, which developed much of the southern coast. Does this mean Crimea belongs to Italy?

You could say Crimea should belong to Russia, but historically, all of Ukraine belonged to Russia (as did much of Eastern Europe)! What justifies the existence of the Ukranian state at all?

And although I'm somewhat breaking this sub's 20-year rule, I'd also like to note that the current Crimean crisis is in great part rendered more complex by the presence of ethnic Russians relocated to Crimea under Soviet Rule, the same way that ethnic Russians were moved around most Soviet Republics (especially to those areas considered industrially or militarily important)

Historically? Depends on how far back in history you go to, Crimea belonged to the Ottomans which Russia then annexed by 1783. Russia then ceded control of the territory to Ukraine on 1954, the reasons for which were:

(1) the cession of Crimea was a “noble act on the part of the Russian people” to commemorate the 300th anniversary of the “reunification of Ukraine with Russia” (a reference to the Treaty of Pereyaslav signed in 1654 by representatives of the Ukrainian Cossack Hetmanate and Tsar Aleksei I of Muscovy) and to “evince the boundless trust and love the Russian people feel toward the Ukrainian people”; and

(2) the transfer was a natural outgrowth of the “territorial proximity of Crimea to Ukraine, the commonalities of their economies, and the close agricultural and cultural ties between the Crimean oblast and the UkrSSS.”

(Source: http://www.wilsoncenter.org/publication/why-did-russia-give-away-crimea-sixty-years-ago)

However the legitimacy of the USSR giving away is definitely flimsy as there was no referendum held, and only 13 of the 27 members of the Supreme Council were present. Nonetheless, about half of Crimea's population is Russian, and from referendums are overwhelmingly in favor of Russia reintegration (both their 1991 and 2014 referendums had 90%+ in favor of reintegration).

So to answer your question, historically (and legally) Ukraine since the USSR officially ceded it to Ukraine. However Crimea's population disagree (or disagreed seeing as how they're no longer under Ukraine control)