I have no idea to this day what those two Italian ladies were singing about.

直到今天我都没有搞懂那两个意大利女人在唱什么.

I have no idea...:used to emphasiza that you don't know anything about sth (表示对某事一无所知)
I had no idea Alex was coming this afternoon.
我一点儿也不知道亚历克斯下午会来.
'What's she talking about?' 'I've no idea.'
"她在讲什么?""我一点也不了解."

to this:day even now, when a lot of time has passed 直到如今;甚至现在
To this day, I still don't understand why he did it.
我直到今天仍然不明白他当时为什么那样做.