Ahh. Here's a good start:

The country’s ultranationalist groups came to the fore in 2014, when they kickstarted massive street protests that led to the ousting of the Russia-friendly president Viktor Yanukovych...

Torch-bearing ultra-right activists regularly march to the beat of drums across the Ukrainian capital’s downtown, chanting, “Death to traitors of Ukraine!” During one scuffle at the memorial to a Red Army general killed in the second world war, an elderly woman approached a group of radical nationalists shouting, “Hang the Russians!” and defied them, saying: “I’m Russian, hang me!”...

In a series of violent actions that underline their strength, rightwing radicals in recent years have assaulted gatherings by LGBT and women’s rights activists, attacked Roma encampments around the country, derailed a lecture on the history of the Holocaust and brawled with pro-Russia veterans...

Yermolayev said in the past the government turned a blind eye to the rise of nationalist groups, using them as a scare tactic, but now the ultra-right has turned on the authorities. “The well-organised and aggressive nationalism in Ukraine is a child of the government. It has lost control over radical nationalists. [Petro] Poroshenko has lost that game.”...

International human rights groups have strongly criticised the Ukrainian government for failing to track down and punish those responsible for the acts of violence and intimidation. The government has promised to rein in the ultranationalists, but has taken no action...

That's a pretty good overview of the character of Ukraine's neo-Nazis, as well as some on the scale of the problem. It mentions they sent "volunteer battalions" to the separatist regions, but does not have tons of detail on what they were doing there. This one has more detail on that:

"I have nothing against Russian nationalists, or a great Russia," said Dmitry, as we sped through the dark Mariupol night in a pickup truck, a machine gunner positioned in the back. "But Putin's not even a Russian. Putin's a Jew."

Dmitry – which he said is not his real name – is a native of east Ukraine and a member of the Azov battalion, a volunteer grouping that has been doing much of the frontline fighting in Ukraine's war with pro-Russia separatists. The Azov, one of many volunteer brigades to fight alongside the Ukrainian army in the east of the country, has developed a reputation for fearlessness in battle...

In this next section, note how the neo-Nazis are declaring they'll do whatever they want, and see themselves as held back by the actual military:

For the commanders and the generals in Kiev, who many in Azov and other volunteer battalions see as responsible for the awful losses the Ukrainian army has suffered in recent weeks, especially in the ill-fated retreat from Ilovaysk, there was only contempt. "Generals like those in charge of Ilovaysk should be imprisoned for treason," said Skillt. "Heads are going to roll for sure, I think there will be a battle for power."

The Ukrainian armed forces are "an army of lions led by a sheep", said Dmitry, and there is only so long that dynamic can continue. With so many armed, battle-hardened and angry young men coming back from the front, there is a danger that the rolling of heads could be more than a metaphor.

And of course:

This week, Amnesty International called on the Ukrainian government to investigate rights abuses and possible executions by the Aidar, another battalion.

"The failure to stop abuses and possible war crimes by volunteer battalions risks significantly aggravating tensions in the east of the country and undermining the proclaimed intentions of the new Ukrainian authorities to strengthen and uphold the rule of law more broadly," said Salil Shetty, Amnesty International secretary general, in Kiev.