  Understanding the physics of rotation-powered millisecond pulsars (MSPs)
presents a number of challenges compared to that of the non-recycled pulsar
population. Even though their fast rotation rates can produce high spin-down
power and accelerating electric fields, their relatively low surface magnetic
fields make the production of electron-positron pairs required for radio
emission difficult. The Fermi Gamma-Ray Space Telescope has discovered pulsed
W-rays from a large fraction of the MSP population that have light curves
surprisingly similar to those of young pulsars. However, their very compact
magnetospheres enable magnetic fields at the light cylinder that are comparable
to those of the most energetic pulsars. This fact and recent global
magnetosphere models showing that particle acceleration takes place near and
beyond the light cylinder, now makes the W-rays from MSPs plausible. The large
increase in binary systems harboring MSPs has revitalized the study of shock
acceleration and high-energy emission in such systems, with many showing
orbitally-modulated X-rays. This Chapter will review the history and our
current studies of the mechanisms for multiwavelength emission from MSPs.
