While emergent behaviours have long been reported for air-breathing osteichthyians, only recently have researchers undertaken quantitative analyses of terrestrial locomotion. This review summarizes studies of sustained periodic terrestrial movements by air-breathing fishes and quantifies the contributions of the paired appendages and the axial body to forward propulsion. Elongate fishes with axial-based locomotion, e.g. the ropefish Erpetoichthys calabaricus, generate an anterior-to-posterior wave of undulation that travels down the axial musculoskeletal system and pushes the body against the substratum at multiple points. In contrast, appendage-based locomotors, e.g. the barred mudskipper Periophthalmus argentilineatus, produce no axial bending during sustained locomotion, but instead use repeated protraction–retraction cycles of the pectoral fins to elevate the centre of mass and propel the entire body anteriorly. Fishes that use an axial–appendage-based mechanism, e.g. walking catfishes Clarias spp., produce side-to-side, whole-body bending in co-ordination with protraction–retraction cycles of the pectoral fins. Once the body is maximally bent to one side, the tail is pressed against the substratum and drawn back through the mid-sagittal plane, which elevates the centre of mass and rotates it about a fulcrum formed by the pectoral fin and the ground. Although appendage-based terrestrial locomotion appears to be rare in osteichthyians, many different species appear to have converged upon functionally similar axial-based and axial–appendage-based movements. Based on common forms observed across divergent taxa, it appears that dorsoventral compression of the body, elongation of the axial skeleton or the presence of robust pectoral fins can facilitate effective terrestrial movement by air-breathing fishes.