Commonly a person's great-niece and nephew are father and daughter. However, they can also be uncle and niece. Technically, what people call a great-niece is actually a grand-niece. There is also a great grand-niece, which is the child of one's grand-niece or grand-nephew.
In order of legal descendants in the U.S., a nephew is seventh in line, while a great-niece is tenth in line. A person's aunt or uncle and great-grandparent are in line between a nephew and great-niece, respectively. This legal precedence comes into play in next-of-kin situations when an estate is in limbo or a medical decision needs to be made.