Conduction is an exchange of energy by direct interaction between molecules of a substance containing temperature differences. It occurs in gases, liquids, or solids and has a strong basis in the molecular kinetic theory of physics.
Radiation is a transfer of thermal energy in the form of electromagnetic waves emitted by atomic and subatomic agitation at the surface of a body. Like all electromagnetic waves (light, X-rays, microwaves), thermal radiation travels at the speed of light, passing most easily through a vacuum or a nearly "transparent" gas such as oxygen or nitrogen. Liquids, "participating" gases such as carbon dioxide and water vapor, and glasses transmit only a portion of incident radiation. Most other solids are essentially opaque to radiation. The analysis of thermal radiation has a strong theoretical basis in physics, beginning with the work of Maxwell and of Planck.
Convection may be described as conduction in a fluid as enhanced by the motion of the fluid. It may not be a truly independent mode, but convection is the most heavily studied problem in heat transfer: More than three-quarters of all published heat transfer papers deal with convection. This is because convection is a difficult subject, being strongly influenced by geometry, turbulence, and fluid properties.
A given problem may, of course, involve two or even all three modes.
[from White, Frank M., Heat Transfer]