くる

来る means "come": movement toward where the speaker is, or toward the place being talked about. The destination takes に or へ. It is irregular, and the vowel changes from form to form: きます来ます is きます, こない来ない is こない, きた来た is きた.

The full set of forms is in the table above. The kanji never changes, so the form tells you the reading: 来ない is こない, never ×くない.

来る or 行く

来る is movement toward the speaker; いく行く is movement away. English says "I'm coming" when you go to the listener; Japanese says 行く, because you are leaving where you are.

• × 今すぐそっちに来ます → 今すぐそっちに行きます

来ている is "is here"

きている来ている is the state after arriving: "has come, is here". It is not "is coming".

For "will be here soon", say もうすぐくる来る.

Usage notes

These go beyond coming to a place.

Coming to do something

A verb's ます-stem with に gives the purpose: "come to do".

After a て-form

After a て-form, てくる means "go and come back" or "bring": もってくる持ってくる, "bring", かって買ってくる, "go and buy". That is a separate grammar point.