I've always been interested in older things before my time, be that games, movies, anime/manga etc. so I've read quite a lot of what most would consider to be the classics in the world of manga. That being said; there is one I've still yet to get to, and that's a manga called Babel II. You don't hear much about it amongst the English speaking sides of manga fan bases, but in Japan, amongst a certain generation, it's quite revered as an influential classic of the Sci-Fi genre. Even people like Hirohiko Araki have cited it as being a major influence on his work.
In terms of a 'modern classic', I must admit that to this day I've still never caught up with One Piece. I thought it was impossible to catch up back in like 2012, I can't imagine trying to catch up to it now lol. Kingdom is another similar one, there's just way too much to catch up on.