Why are some agricultural fields circular (especially in the midwest)?

On the last few flights I've taken across the country, I've noticed that once the plane is over the midwest, when I look down, many of the fields are circular. You can see that the boundaries are square, but then there is a green circle of irrigated crops inscribed in the brown square. I noticed this somewhere over colorado and it seemed to be true as we flew over a number of midwestern states..by the time we got to the east coast the fields were planted in full squares again. Is this due to some kind of irrigation technique? Might it have to do with the biblical command to leave the corners of your field for the poor? I really have no idea.