traer/llevar

traer - to bring something from point A to point B. To use traer, the speaker needs to be at point B
llevar - to bring something from point A to point B. To use llevar, the speaker can't be at point B.

The most obvious examples for me:
you're at a party and you call someone to bring ice:

¿Podis traer hielo? Se nos acabó.
Can you bring ice? It ran out.

you're on your way to a party and you call to see what to bring:

¿Qué llevo? Coca-cola? hielo? What should I bring? Coke? Ice?

also I hear people use "lo ando trayendo" and sometimes "lo ando llevando".

María: ¿Tenis el examen del año pasado?
el Tata: si, lo ando trayendo.

María: Do you have the exam?
el Tata: Yes, I have it with me.

General Spanish

*Thanks Clare, for the suggestion.