Hagfishes have both intrigued and confused biologists since Linnaeus first mistakenly classified one as an "intestinal worm." Modern hagfishes (Myxinidae) are elongate, marine fishes often described by what they lack: jaws, scales, paired fins, or a vertebral column. Accompanying this reduced morphology was a long-held view that hagfish are lazy animals that mostly lay about on the ocean floor, but more recent research has revealed them to be active hunters and scavengers in the benthic community. Routine swimming is a requisite part of these activities, yet knowledge of how these exceptionally flexible fishes swim is limited. Here, I use an integrative experimental approach to provide a more comprehensive, quantitative understanding of locomotory mechanisms in hagfishes. In Chapters 1 and 2, I use high-speed videography to quantify whole-body kinematics of steady and unsteady swimming in Eptatretus stoutii and Myxine glutinosa, representing the two main lineages within Myxinidae. Both species generally swim with high amplitude head movements and use tail beat frequency to control swim speed, but inter- and intra-specific variation in other undulatory wave variables suggests multiple mechanisms to modulate speed. Changes in the shape of the body wave characterize the observed unsteady swimming behaviors. During positive linear accelerations, hagfish transiently adopt a larger, longer body wave. During lateral maneuvers, hagfish approximate “sidewinding” behavior as anterior body regions interact with the substrate while posterior body regions propagate waves of lateral bending toward the tail tip. Chapter 3 integrates kinematics with hydrodynamics, using particle image velocimetry to visualize the flow field around swimming E. stoutii. The steady swimming wake consists of caudolateral fluid jets, which turn caudally during linear accelerations. Wake jets orient asymmetrically during lateral swimming, contributing both forward and lateral thrust over a complete tail beat. The hydrodynamic patterns observed reinforce kinematics-based hypotheses on how hagfishes enact their various swimming behaviors. In Chapter 4, I use simple robotically-controlled physical models to examine functional relationships between body flexural stiffness, shape, kinematics, hydrodynamics, and swimming performance. I relate model swim performance to characteristics of hagfish swimming, and describe lessons that passively undulating models impart for understanding locomotion by live elongate undulatory swimmers.