The Beginning
[I.63] Pestilences extinguished, the world becomes smaller, for a long time the lands will be inhabited peacefully. People will travel safely through the sky, land and seas : then wars will start up again
This quatrain is considered to be the quatrain which indicate the start of WW-III. The scenario described in this quatrain is definitely a modern world scenario as is describes air travel. Air travel became commercially available only after WW-II. World is a small place now with ease of communications. Antibiotics helped man to get rid of many incurable diseases. But, Nostradamus says, wars will start up again. Alternatively, this might describe a period of unparalleled peace predicted after WW-III when the Great Monarch will reign, till the "End of the World".
The fall of communism
[IV.32] In those times and places that meat gives way to fish the law of commune will be opposed. The old order will hold strong, then removed from the scene, then all things common among friends put far behind
We have already seen this prophecy coming true. During the early 1990s in Soviet Union and
Communist Europe (in those times and places), when the economic condition in these countries deteriorated (meat gave way to fish), Communism (the law of commune) was opposed by the people. The old leaders indeed tried to hold on but ultimately were removed from powers.
Ultimately Communism (all things common among friends - equality among friends - comrades) collapsed. This prophecy was understood even before its accomplishment by many interpreters. But the instability caused by collapse of USSR and the resulting unipolar world may indirectly be the cause of the next great war.
The attack on New-York
[VI.97] The sky will burn at 5 and 40 degrees, fire approaches the great New City.
Immediately a huge, scattered flame leaps up when they want to have proof of the Normans
Probably this quatrain describes a nuclear attack on