Light transport in a highly multimode fiber exhibits complex behavior in space, time, frequency, and polarization, especially in the presence of mode coupling. The newly developed techniques of spatial wavefront shaping turn out to be highly suitable to harness such enormous complexity: a spatial light modulator enables precise characterization of field propagation through a multimode fiber, and by adjusting the incident wavefront it can accurately tailor the transmitted spatial pattern, temporal profile, and polarization state. This unprecedented control leads to multimode fiber applications in imaging, endoscopy, optical trapping, and microfabrication. Furthermore, the output speckle pattern from a multimode fiber encodes spatial, temporal, spectral, and polarization properties of the input light, allowing such information to be retrieved from spatial measurements only. This article provides an overview of recent advances and breakthroughs in controlling light propagation in multimode fibers, and discusses newly emerging applications.