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Nanorobotics encompasses the design, fabrication, and programming of robots with overall dimensions below a few micrometers, and the programmable assembly of nanoscale objects. Nanorobots are quintessential nanoelectromechanical systems (NEMS) and raise all the important issues that must be addressed in NEMS design: sensing, actuation, control, communications, power, and interfacing across spatial scales and between the organic/inorganic and biotic/abiotic realms. Nanorobots are expected to have revolutionary applications in such areas as environmental monitoring and health care. This paper begins by discussing nanorobot construction, which is still at an embryonic stage. The emphasis is on nanomachines, an area which has seen a spate of rapid progress over the last few years. Nanoactuators will be essential components of future NEMS. The paper's focus then changes to nanoassembly by manipulation with scanning probe microscopes (SPMs), which is a relatively well established process for prototyping nanosystems. Prototyping of nanodevices and systems is important for design validation, parameter optimization and sensitivity studies. Nanomanipulation also has applications in repair and modification of nanostructures built by other means. High-throughput SPM manipulation may be achieved by using multitip arrays. Experimental results are presented which show that interactive SPM manipulation can be used to accurately and reliably position molecular-sized components. These can then be linked by chemical or physical means to form subassemblies, which in turn can be further manipulated. Applications in building wires, single-electron transistors, and nanowaveguides are presented.