Italy's growth rate with new cases is decreasing, that's the main thing. It looks like it has peaked within 2 weeks of lockdown as expected. Now the total number of cases will still increase for another 9 or 10 days sadly because even though the number of new cases will fall now it will still outnumber the recoveries. After that the recoveries should start to outnumber new cases and the number of active cases will fall rapidly.
I think Italy will get to about 120k cases from this wave and the deaths will get to close to 20k.
The deaths are so high there because the Italian authorities are reporting deaths in a different way to many other countries.
The New York outbreak is really horrific and looking like it will be much worse that Italy, a huge price paid for extremely slow testing and delay in lockdown and other measures. They're at least 10 days from the peak and already having more than 5k new cases a day. The peak there might be 15k cases in a single day, maybe even more.
Governor Cuomo has said they need 40,000 ICU beds within 3 weeks. For comparison there are 2,200 ICU beds in the whole of Australia.