When a spin-polarized current interacts with a magnet, it can transfer spin angular momentum to the magnet and thereby apply a torque. This spin-transfer effect can be used to manipulate the magnetic-moment direction of small magnets much more efficiently than using magnetic fields. I will describe experiments which utilize 100-nm-scale magnetic devices to investigate the microscopic origin of this effect and the ways in which individual nanomagnets can respond to the torque. I will also discuss progress on extending these experiments to the molecular scale, and some unexpected new magnetic phenomena that this work has revealed.