At a briefing in their war room on Monday, the two Ukrainian generals responsible for the defence of Kyiv told the BBC how their forces were fighting hard to keep Russian artillery out of range, and explained why they believe the city has strengths that will make all the difference against the Russians.
Kyiv is feeling the sharp touch of the war more acutely, along with Russia's destructive firepower.
A nine-storey block of flats was hit by a Russian missile on Monday morning, killing at least one person and wrecking the building, making dozens of Ukrainians homeless. It would have been worse had many residents not taken to shelters.
But the centre of Kyiv and many of its sprawling suburbs are still untouched by Russian weaponry. Other Ukrainian cities are being very heavily shelled, and there have been many casualties.
Kyiv's remaining citizens - perhaps half have moved to western Ukraine or left the country - are facing the possibility that the same brutal experience lies ahead for them.
The generals responsible for Kyiv's defence said they were fighting hard to keep Russian artillery out of range, but accepted that the capital was vulnerable to missiles.
However the city's topography and terrain is on their side, Gen Andriy Krischenko told me. The city is big and sprawling. It is cut up by rivers, not just the mighty Dnieper which divides Kyiv in two, but its tributaries.
"It is difficult to defend on the one hand, given that it is very large," he told me. "But on the other hand, this is a plus. Rivers, bridges, are on the approaches to the city. Our troops are building defences and fortifications.
"Around the city there are many small rivers that flow into the Dnieper and there are many peat bogs, so that means the area is not suitable for large-scale movement of troops."
Gen Krischenko, who is also a deputy mayor, was wearing the same kind of informal outfit in army green that his President Volodymyr Zelensky has worn to rally his people, impress his allies and infuriate his enemies. The general also exuded the president's optimism.
Another advantage, according to the general, is that Kyiv is an industrial city, with workshops and factories that have repurposed themselves to produce the items needed for fortifications - concrete blocks, sandbags, and a variety of savage-looking anti-tank obstacles.
Gen Krischenko and Gen Knyazev stood in front of the big interactive screen they use to track the Russian push towards Kyiv.
They explained they had attacked and stopped the forward movement of two main thrusts, one from the east and one from the north-west, which included the much talked about 64km (40 mile) column of Russian armour.
They said it had been attacked and forced to disperse, and insisted it was no longer a threat.
The north-west is still the Russians' main focus. Gen Knyazev pointed to what he said was the closest force of Russian infantry. It was the other side of the Irpin River, around 20km (12 miles) from central Kyiv.
The Ukrainians have deployed a well-organised and well-armed force, which has blown strategic bridges. Thousands of people displaced from the town of Irpin have been filing over the river on the remains of the one of them with a few possessions and very often, their dogs and cats.
But the Russians, said Gen Knyazev, have not been able to follow them.
"These are such marshy lowlands, and they can't pass them. If there were no Ukrainian soldiers, they would simply throw a pontoon crossing over the river. But we are there, and we want to destroy them."
As we were talking another missile exploded not far from the first one. The noise of the blast could be heard clearly in the war room. "Listen," said a junior officer, "that was our air defence bringing down another one."
But it did not take the missile out in mid-air. A trolley bus conductor was killed when it hit the ground with a big explosion that also wrecked a line of buildings.
Ukrainian military success has surprised their friends, and their enemies. The president and his commanders are more than pleased with the performance of their army and thousands of volunteers.
But the Russians have not turned anything like their full force on this capital city yet.