To possess information
be aware of, be cognizant of, be acquainted with, be informed, be in possession of the facts, have knowledge of, be schooled in, be read in, be learned in, be versed in, be conversant with, be familiar with, appreciate, prize, ken, recognize, be sensible of, know full well, be sure of, have at one's fingertips, be master of, have a grasp of, know by heart, know inside and out, know by rote, remember, be instructed, be awake to, keep up on, have information about, know what's what, know all the answers, have someone's number*, have the jump on*, have down cold*, have the goods on*, be hep to*, know one's stuff*, know the score*, know the ropes*.
Antonyms be oblivious of, be ignorant of, misunderstand.