Quantum Electrodynamics (QED)
What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school … It is my task to convince you not to turn away because you don't understand it. You see my physics students don't understand it … That is because I don't understand it. Nobody does.
I didn't write this, but I intend to write something like this.
On a microscopic level, all four forces are not forces in the usual sense of the word. The way that physics today explains the forces of nature is by exchange of gauge particles. Gauge particles are particles which are exchanged between other particles that form the genuine constituents of matter (quarks and leptons). So when an electron repels or attracts another electron or positron, what happens is that there is a "force-carrying field" between them. In that particular case, it is actually a field composed of photons! Photons are the mediators of the electromagnetic interaction, and particles interacting electromagnetically constantly exchange photons between them (those photons can not be "seen" in the usual sense, but that is another story). Now when an electron emits or absorbs a photon, it more or less stays the same, only its momentum and spin might change.