Inspired by the highly efficient biological motors in nature, researchers proposed the concept of micro/nanomotors, or micro/nanoscale autonomously moving devices. Combining the technology of chemistry, physics and multidisciplines, various micro/nanomotors of different structures, motion mechanisms and control methods are fabricated. These micro/nanomotors demonstrate great promises in multiple fields including sensing, environment remediation, biomedicine, etc. One of the most important applications in biomedicine is drug delivery. The micro/nanomotors can achieve efficient drug delivery, shedding new light for conventional cancer therapy. In this review, we focus on micro/nanomotors for drug delivery and introduce their structures, mechanisms and control methods. The motion mechanisms(self field mechanism and external field mechanism) of micro/nanomotors will be covered. Motor structures(polymer vesicle, tube and nanowire) suitable for drug delivery will be introduced. For efficient targeted drug delivery, motion control is very important. The on-off control, direction control and velocity control will be discussed. Current bottlenecks are also summarized and possible future direction of the field is discussed.