A blind riveting apparatus (1) comprises a motor (3), and a clamp (31) for gripping the mandrel of a blind rivet, the clamp being movable substantially along the axis of the rivet. The apparatus further comprises a first transmission (51) configured to transfer rotary motion of the motor (3) to the clamp (31) when engaged; and a second transmission (52) configured to convert rotary motion of the motor (3) to linear motion of the clamp (31), and thereby retract the clamp (31) to pull on the mandrel, when engaged. A transmission control apparatus is arranged to selectively adjust the degree of engagement of at least one of the first (51) and second (52) transmissions, the transmission control apparatus comprising a variable-influence brake or clutch (58). Methods of blind riveting, and further pieces of blind riveting apparatus, are also disclosed.