"Kilayim" and "kilay hakerem" are two classes of prohibitions on eating from "mixed" fields (in which more than one type of crop is planted.) "Kilayim," as I understand it, specifically refers to the prohibition on wheat and barley grown together, whereas "Kilay Hakerem" refers to a prohibition on "eating from a vineyard with other seeds mixed into it."
According to the Mishna (Kidushin ch.1, #9), these laws are not actually restricted to the land of Israel, but must be observed worldwide, since they are halacha l'Moshe mi-Sinai.
So how do we know that fruit, vegetables, wheat, barley etc. that are sold commercially outside of Israel (without a hechsher) follow these laws? If not, why are we allowed to eat from them?