Surface electromyography (sEMG) is a non-invasive method of measuring neuromuscular potentials generated when the brain instructs the body to perform both fine and coarse locomotion. This technique has seen extensive investigation over the last two decades, with significant advances in both the hardware and signal processing methods used to collect and analyze sEMG signals. While early work focused mainly on medical applications, there has been growing interest in utilizing sEMG as a sensing modality to enable next-generation, high-bandwidth, and natural human-machine interfaces. In the first part of this review, we briefly overview the human skeletomuscular physiology that gives rise to sEMG signals followed by a review of developments in sEMG acquisition hardware. Special attention is paid towards the fidelity of these devices as well as form factor, as recent advances have pushed the limits of user comfort and high-bandwidth acquisition. In the second half of the article, we explore work quantifying the information content of natural human gestures and then review the various signal processing and machine learning methods developed to extract information in sEMG signals. Finally, we discuss the future outlook in this field, highlighting the key gaps in current methods to enable seamless natural interactions between humans and machines.