The campaign targets have been high profile.
St Petersburg was hit with drones ahead of Putin’s showpiece economic forum in June. Then there were strikes on Moscow itself, creating explosion videos that went viral.
Now there’s a confirmed hit on an oil refinery in Omsk, Siberia, 2,500 km from Ukraine’s border. The drone must have flown undetected for many hours, which shows how stretched Russia’s own air defences actually are.
Ukraine’s “influence” efforts also include Crimea, the peninsula which Putin seized in 2014 and which is deeply important to him personally.
Ukrainian drones are now hitting military logistics, oil refineries and power plants there almost every day, causing power cuts, fuel and food shortages and an official state of emergency.
A local resident told the BBC the situation was “catastrophic”, reminiscent of the turbulent 1990s after the USSR collapsed.
One of Putin’s great claims is that he “saved” the country from that chaos, raising Russia “from its knees”.
Now his all-out war is bringing danger even to Moscow in the form of drone strikes, and widespread fuel rationing.
So Zelensky will tell Nato, and try to persuade Trump, that Ukraine has turned the tide in this war, and that its campaign of pressure can, with help, compel Russia to engage in proper negotiations for peace.
Trump has seemed impressed by Ukraine lately, although he spoke to Putin for 90 minutes by phone this week, giving the Russian leader a chance to get his war story in first.
Above all, Kyiv wants to end this war fast, through “strength or diplomacy”, before another gruelling winter kicks in.
But to have any chance of that, Zelensky will argue, Ukraine needs more interceptor missiles to protect its cities and civilians.
