In many beginning Japanese classes, 来る【くる】 and 行く【いく】 are presented as "to come" and "to go," respectively. Dictionaries generally also define them this way. However, every once in a while in more advanced classes, teachers will mention that this is not actually the case; these words are used differently in Japanese than their English (pseudo-)counterparts.
I cannot for the life of me remember the proper way to understand the differentiation between these verbs, past "come" and "go," a fact which is most embarassing.
Can someone please explain how these words are different than the English "come" and "go" in their usage?
Related question: Difference between -て行く and -て来る