Since 2014, it's clear that Russian troops have invaded Ukrainian territory. Crimea was fully annexed and the Donbass is in a state of perpetual conflict. However, officially speaking, Russia and Ukraine didn't declare war on each other and do maintain diplomatic relations.
What is the reason behind this?
Russia cannot declare war officially:
In total, military help and support for pro-russian armies is cheaper, and more importantly, gives Russia no responsibility over what the armies do. If the status quo is held for enough time, the pro-russian territories will become part of Russia anyway.
Ukraine cannot declare war officially:
In summary, Russia did attack Ukraine in a smart way, giving Ukraine no way to attack back.
Ukraine could technically ask UN to interfere but Russia has the right to veto everything therefore there is nothing Ukraine can do.
Currently there is no power in the world that could force Russia to give Crimea back. Russia cannot be fought militarily because that would require the help of at least 2 other great powers (e.g. USA and China), technically triggering WW III with probable nuclear outcome.
War is the continuation of politics by other means - Carl von Clausewitz.
Practically all state actors in international politics are rational. Certainly there are exceptions, e.g. Nazi Germany after Barbarossa, Fascist Japan after Pearl Harbor, etc. But even North Korea has some rationale for their actions.
Therefore, countries don't fight each other because they want to, but because they see it as a way to "get what they want", i.e. to achieve their political agenda. This is why most wars in human history have been rather limited; total war break out only when both sides know that absolutely no deal can be made.
Now, does this apply to Russia and Ukraine? Certainly not. Russia needs to make a deal some time as the war would make them look bad and likely result in sanctions, plus they just can't (and aren't interested) in occupying, not to mention annexing, Ukraine. Russia's priorities are keeping Ukraine away from the West (or better, pro-Russia), and keeping Crimea, as it is strategically important for Russia. Ukraine's priorities are maintaining its own territorial integrity to the greatest extent, and they'd be more willing than anyone to make a deal (they just don't stand a chance if war escalates).
Since both sides are "gentlemen" and are looking for a deal, why escalate things to the point of official state of war? It's just they couldn't yet reach a deal, but they'd have to arrive at one some time later. War is a very costly way to do politics, and they can't do it for too long, especially if both sides don't have too much money to spare.
The UN Charter prohibits both the threat and the use of force in international conflicts.
https://www.un.org/en/sections/un-charter/chapter-i/index.html
Which means that formally declaring war by one country on another is illegal under international law.
That's why virtually nobody declares war anymore. Countries just attack each other, without any formal declarations of war. And they rationalize their violence in some way to make it look consistent with international law.
In USA for example, only the US Congress has the Constitutional right to declare war. And last time this happened was in 1941, after Japan attacked Pearl Harbor.
But USA has been involved in many wars since then anyway. And the US Congress has looked the other way. This is probably because declaring war is now illegal under international law, that USA has agreed to abide by.
Ukrainian government directly calls the conflict a war in media, and the question of state of war had been raised for several times already. Although, the government wouldn't want to go for it, since it gives Poroshenko a total control over the state, and the civil rebel might follow.
Neither Ukraine nor Russia want to enter into an official war with each other. Russia does not need to do so. Invading and occupying the whole of Ukraine would be very expensive - too expensive for Russia. It would be an act of aggression - and waging aggressive war is a war crime. It would irreparably damage Russia's relations with the EU and very likely also with most of the rest of the world. Also, Russia does not want to have bad relations with Ukraine, it was forced into the current conflict by the need to protect its vital national interests in the Black Sea. The Donbass and Luhansk insurgencies started on their own and Russia got involved only to protect the Russian-speaking majority in those regions from annihilation by Ukraine's military and paramilitary forces, after the May 3, 2014 massacre in Odessa. Russia would like very much to end the whole situation peacefully and be again on speaking terms with Ukraine and the EU. A major obstacle is, of course, Crimea - Russia will never return it as most Russians (and Crimeans) see Crimea historically as Russian territory. Unless a deal is made on Crimea (most likely where Russia makes major economic concessions to Ukraine in return for Ukraine accepting the permanent loss of Crimea), the political situation in Europe will not improve significantly.
Ukraine, on the other hand, has a good argument for waging war on Russia (loss of Crimea, very likely Russian support for insurgents in Donbass and Luhansk), but sees that it would be folly. Its military is decidedly inferior to Russian military. Also, there are still major parts of Ukraine with significant percentage of Russian-speaking population, which would likely rise in insurgency in case of major Russo-Ukrainian armed conflict. Also, increase in violence would further complicate Ukrainian efforts in EU integration.
With the rising Ukrainian nationalism and the increasingly more and more visible loss of control of the central government over the country (in the recent trade blockade of Donbass by Ukrainian nationalists, president Poroshenko protested the blockade but was unable to force its lifting), it is possible that Ukrainian military will take more forceful action against Donbass and Luhansk, which may force Russia's hand, so not all risk of war is beyond us. I hope it is not necessary to mention what a tragedy that would be for Ukraine and Russia both and that it would leave the political situation in Europe even more strained, possibly for decades. No matter what anybody says, Ukraine and Russia are important parts of Europe and real, all-out war between them is too terrible to contemplate.
