Quantum Phase Transitions and Exotic Phases in the Metallic Helimagnet MnSi

Helimagnets are magnetically ordered materials in which the spin-orbit interaction leads to a spiral structure of the magnetization. I will review the phenomenology of MnSi as the prototypical and best studied helimagnet, in particular various phases or suspected phases identified by neutron scattering and other techniques. The most spectacular feature is a pronounced T^(3/2) behavior of the resistivity in a large region of parameter space. I will then review theoretical efforts to understand the observed effects. The nature of the ordered phase is well understood, and interesting analogies with liquid crystals allow for an understanding of the structure of the phase diagram. The transport properties are still largely mysterious, however.