Hands are vital in a wide range of fundamental daily activities, and neurological diseases that impede hand function can significantly affect quality of life. Wearable hand gesture interfaces hold promise to restore and assist hand function and to enhance human-human and human-computer communication. The purpose of this review was to synthesize current novel sensing interfaces and algorithms for hand gesture recognition, and the scope of applications covers rehabilitation, prosthesis control, sign language recognition, and human-computer interaction. Results showed that electrical, dynamic, acoustical/vibratory, and optical sensing were the primary input modalities in gesture recognition interfaces. Two categories of algorithms were identified: 1) classification algorithms for predefined, fixed hand poses and 2) regression algorithms for continuous finger and wrist joint angles. Conventional machine learning algorithms, including linear discriminant analysis, support vector machines, random forests, and non-negative matrix factorization, have been widely used for a variety of gesture recognition applications, and deep learning algorithms have more recently been applied to further facilitate the complex relationship between sensor signals and multi-articulated hand postures. Future research should focus on increasing recognition accuracy with larger hand gesture datasets, improving reliability and robustness for daily use outside of the laboratory, and developing softer, less obtrusive interfaces.