Signed languages are the primary means of communication for many deaf and hard-of-hearing individuals. Since signed languages exhibit all the fundamental linguistic properties of natural language, we believe that tools and theories of Natural Language Processing (NLP) are crucial for its modeling. However, existing research in Sign Language Processing (SLP) seldom attempts to explore and leverage the linguistic organization of signed languages. In this talk, I will talk about why I believe NLP researchers should include signed languages in their research and some of the challenges in sign language processing today. I will also cover two projects that take steps in extending NLP to signed languages: data augmentation for sign language translation and coreference resolution for pronominal indexing signs. Through these examples, I will illustrate that NLP plays a crucial role in the development of sign language processing systems.