Extra sensory perception is defined by the American Psychological Association (APA) Dictionary of Psychology as "Alleged awareness of external events by other means than the known sensory cannels. It includes telepathy, clairvoyance, precognition, and, more loosely psychokinesis.
Despite considerable research, the existence of any of these modalities remains highly controversial".

The term ESP was popularized by J. B. Rhine, who began investigating paranormal phenomena at Duke University in 1927.

When I did a google search on ESP communication experiments, I found a lot of books, "Multidimensional Mind: Remote Viewing and the Evolution of Intelligence" and articles like "Extrasensory Communication and Dreams", "Extra Sensory Perception (Esp) And Horses".

I am a skeptic, and not convinced about experiments with people in altered mental states, whether in meditation, dreams, hypnoses, or other.

However, I've heard several stories from rational, trustworthy friends and acquaintances, which can be described as ESP. The most convincing are ones where the sender was someone in a near death or death situation.

Others, including a personal experience, involved chance communication with another person where, in my case a topic poped into my head for no particular reason, and that topic had a unlikely significance to the other person.

predictive psi phenomena

Terms:
ESP - Extrasensory perception -
Precognition - Seeing things in the future.
Premonition - Inner knowledge of something to happen in the future
PK - psychokinesis - Psychokinesis is the process of moving or otherwise affecting physical objects by the mind only
Psi - parapsychology - Processes such as telepathy or other forms of extrasensory perception that are currently unexplained in terms of known physical or biological mechanisms

Links:
Extrasensory Perception (ESP), Science, The Roots of Consciousness
pseudoscience - Psychic powers and ESP
Your Eternal Self Drafts, 2008, R.C. Hogan, Ph.D.
ESP - extrasensory perception - The Skeptic's Dictionary - Skepdic.com