In this thesis, we study the problem of recognizing video sequences of fingerspelled letters in American Sign Language (ASL). Fingerspelling comprises a significant but relatively understudied part of ASL, and recognizing it is challenging for a number of reasons: It involves quick, small motions that are often highly coarticulated; it exhibits significant variation between signers; and there has been a dearth of continuous fingerspelling data collected. In this work, we propose several types of recognition approaches, and explore the signer variation problem. Our best-performing models are segmental (semi-Markov) conditional random fields using deep neural network-based features. In the signer-dependent setting, our recognizers achieve up to about 8% letter error rates. The signer-independent setting is much more challenging, but with neural network adaptation we achieve up to 17% letter error rates.