Email fighting, is there any law against a person sending you threatening emails?

What can one do if they have problems on an email in which a person makes threatening or mean statements which are upsetting? I responded to a few of them until I just realized I could block the emails but it got me to thinking if there is any legal precedent to sue someone for sending slanderous emails to your inbox and abusive statements? It is not work related but personal. Let me know of any cases or times that this type of email is resolved with more than just blocking it. It was not life threatening but they intimated that they would try to cause problems to a family member at work.