Reports say an attack is underway on an airport around 40 kilometres outside Kyiv.
There are reports of explosions and shelling in several cities in Ukraine, with regional authorities saying a number of people have died.
Images show Ukrainians queuing up to join the military or give blood.
It's prompted a surge in oil prices - which experts warn is likely to result in higher fuel costs.
NATO's secretary general Jens Stoltenberg says the military alliance is prepared:
"We have over 100 jets at high alert, protecting our airspace and more than 120 allied ships at sea from the high north to the Mediterranean Sea."
These people spoke as they fled across the border into Poland:
"This happening to the country is just devastating. I just I just can't believe someone could be so evil."
"I came from Ukraine from Russia. I'm just trying to make something good for my family and hoping that my wife will be safe."