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. a 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.
a In particle physics, a gauge boson is a bosonic elementary particle that mediates interactions among elementary fermions, and thus acts as a force carrier. Gauge bosons can carry any of the four fundamental interactions of nature. Elementary particles, whose interactions are described by a gauge theory, interact with each other by the exchange of gauge bosons; usually as virtual particles. Photons, W and Z bosons, gluons, and the hypothetical gravitons are gauge bosons. All known gauge bosons have a spin of 1; for comparison, the Higgs boson has spin zero. Therefore, all known gauge bosons are vector bosons.