The Ukrainian government has taken back control in one eastern city

On Monday, Ukraine retook control of government buildings in Kharkiv without any blood being shed.

"Ukrainian authorities said it was done without a shot being fired," says the BBC's David Stern. "They said they are going to restore order in eastern Ukraine peacefully, or without any violence. But of course, given the tensions, given the emotions, these may prove to be very difficult."

Protesters are still occupying the administrative buildings in Luhansk and Donetsk. Donetsk is where ousted Ukrainian president Viktor Yanukovych was born. Pro-Russian demonstrators on Monday declared the city, a "people's republic."    

The eastern part of Ukraine is economically important to the country. It's where the mining and metallurgy industries are based, says Stern. "Donesk is sort of the heart of that." 

There's no clear divisions between east and west Ukraine, Stern says. 

"It's also not a clean division between Russian-speakers and Ukrainian-speakers. When we say there are divisions within Ukrainian society, it's not exactly on one side is one side of the country, on the other side, is the other side of the country. It's very much within these locations, within the society itself. So anything that happens is going to be messy."

Stern says that if tensions escalate, it's going to be protracted and, potentially, "it could be very, very bloody."