In much of the world, consanguineous marriage between cousins is very common. In many states, it is illegal for first cousins to get married. The objections are ostensibly based on the risk of genetic problems.
What is it called when you are dating your cousin?
A cousin marriage is a marriage where the spouses are cousins (i.e. people with common grandparents or people who share other fairly recent ancestors). The practice was common in earlier times, and continues to be common in some societies today, though in some jurisdictions such marriages are prohibited.
What happens when you date your cousin?
In the United States, second cousins are legally allowed to marry in every state. However, marriage between first cousins is legal in only about half of the American states. All in all, marrying your cousin or half-sibling will largely depend on the laws where you live and personal and/or cultural beliefs.