The past several years have seen dramatic developments in the study of planetary magnetic fields, including a wealth of new data, mainly from the Galilean satellites and Mars, together with major improvements in our theoretical modeling effort of the dynamo process believed responsible for large planetary fields. These dynamos arise from thermal or compositional convection in fluid regions of large radial extent. The relevant electrical conductivities range from metallic values to values that may be only about 1% or less that of a typical metal, appropriate to ionic fluids and semiconductors. In all planets, the Coriolis force is dynamically important, but slow rotation may be more favorable for a dynamo than fast rotation. The maintenance and persistence of convection appears to be easy in gas giants and ice-rich giants, but is not assured in terrestrial planets because the quite high electrical conductivity of iron-rich cores guarantees a high thermal conductivity (through the Wiedemann-Franz law), which allows for a large core heat flow by conduction alone. In this sense, high electrical conductivity is unfavorable for a dynamo in a metallic core. Planetary dynamos mostly appear to operate with an internal field ∼(2 ρΩ/ σ) 1/2 where ρ is the fluid density, Ω is the planetary rotation rate and σ is the conductivity (SI units). Earth, Ganymede, Jupiter, Saturn, Uranus, Neptune, and maybe Mercury have dynamos, Mars has large remanent magnetism from an ancient dynamo, and the Moon might also require an ancient dynamo. Venus is devoid of a detectable global field but may have had a dynamo in the past. The presence or absence of a dynamo in a terrestrial body (including Ganymede) appears to depend mainly on the thermal histories and energy sources of these bodies, especially the convective state of the silicate mantle and the existence and history of a growing inner solid core. Induced fields observed in Europa and Callisto indicate the strong likelihood of water oceans in these bodies.