1. Accelerate an electron, get a photon. A good transmitting antenna is something that is an efficient structure for accelerating electrons.
2. Antennas are reciprocal. They receive as well as they transmit.
3. Resonant structures are often used because you can keep more electrons accelerating with less energy -- the damp finger on the rim of a wine glass effect.
4. Power can be directed by appropriately phasing the radiating sub-structures to create constructive and destructive interference in the radiated energy.
The rest is modeled simply with a set of simultaneous three dimensional second-order partial differential equations.