Is weed legal in NYC?

I'm curious, what's the current legal status of marijuana possession and use in New York City? I've heard rumors that things might have changed recently, but I'm not sure what the exact regulations are. Can you clarify for me if weed is now legal in NYC, and if so, what are the specific rules and guidelines that govern its use and possession? I'm particularly interested in knowing if there are any penalties for those who don't comply with the law.