Patrick Jane, a detective and independent consultant with the California Bureau of Investigation, used to pretend to be a psychic medium, but now he just uses his powers of observation to solve crimes
Tmk, they have never been out on a date. However, there has been acknowledgement of their feelings both by themselves and by the rest of the team.
They have kissed once in the episode where R was under hypnosis and J told him to do the one thing he most wanted in the world.
They almost kissed in the episode where VP's 'boyfriend' attacks R, and VP goes to help him and they have a little moment which is interrupted.