Dynamics induced by spin-transfer torque is a quickly developing topic in modern magnetism, which has initiated several new approaches to magnetic nanodevices(1-11). It is now well established that a spin-polarized electric current injected into a ferromagnetic layer through a nanocontact exerts a torque on the magnetization, leading to microwave-frequency precession detectable through the magnetoresistance effect. This phenomenon provides a way for the realization of tunable nanometre-size microwave oscillators, the so-called spin-torque nano-oscillators(3,4,6) (STNOs). Present theories of STNOs are mainly based on pioneering works(12,13) predicting emission of spin waves due to the spin torque. Despite intense experimental studies, until now this spin-wave emission has not been observed. Here, we report the first experimental observation and two-dimensional mapping of spin waves emitted by STNOs. We demonstrate that the emission is strongly directional, and the direction of the spin-wave propagation is steerable by the magnetic field. The information about the emitted spin waves obtained in our measurements is of key importance for the understanding of the physics of STNOs, and for the implementation of coupling between individual oscillators mediated by spin waves(9-11,14). Analysis shows that the observed directional emission is a general property inherent to any dynamical system with strongly anisotropic dispersion.