1. Penetration of others' minds and thought-reading (telepathy)
Once on an Uposatha day, the Buddha sat silently throughout the whole night in front of the assembly of monks. When the morning dawned, he only said: "This assembly is impure." Thereupon Moggallana surveyed with his mind the entire assembly from monk to monk and saw that one monk was entirely corrupted. He went towards him and asked him to leave. When that monk did not move though asked thrice, Moggallana took him by the arm, led him out of the hall and bolted the door. Then he begged the Exalted One to recite the Rules of Monastic Discipline (Patimokkha), as the assembly was now pure again. (A. VIII, 20)
Once the Master stayed together with a community of five hundred monks who all were saints. When Moggallana joined them, he at once discerned in his heart that all these monks were canker-freed Arahats. Then one of these saintly monks who, on his part, cognized Moggallana's supernormal perception, rose from his seat and praised Moggallana in the following verses:
"Him who serenely sits on mountain's slope,
a sage who has transcended ill entire —
to him disciples pay their homage,
themselves of triple knowledge, vanquishers of death.
He has discerned them by his mental power,
the master of the supernormal, Moggallana.
He probed their minds with his
and found them free and unattached."
— Samyutta Nikaya 8, 10
A third report says: Once, while the venerable Anuruddha was meditating in solitude, he considered how, by means of the four Foundations of Mindfulness (satipatthana) the Noble Path that leads to the extinction of suffering can be perfected. Then Moggallana, penetrating Anuruddha's mind by his own, appeared before him through supernormal power and requested him to describe in detail this method of practice (Samy. 52, 1-2).