They become a couple at the end of season 9 and continue for a bit in season 10, after which, they decide it would be best to stay best friends.
Their timing had always been a problem, since Joey originally fell in love with Rachel in season 8, but then stepped back because of the fact that Rachel was expecting a baby girl with Ross.
Rachel on the other hand, started developing stronger feelings for Joey a year later, after the infamous dream.
Their relationship has always been filled with sexual chemistry (and remarks by Joey) and genuine love and care for each other.
Some claim there would have been a different ending for the both characters, if it weren`t for the spin off Joey, which included Joey moving to LA and starting fresh.