Matter-antimatter and annihilation In this question, it seems  posed how a particle and its anti particle can get close to each to annihilate. One answer proposed that "The force involved in annihilation is normally either the color force (in the case of quarks/antiquarks) or the electromagnetic force (in the cases of electrons/positrons)."
This, I assume, means that for electrons and positrons, the opposite charges  is a force of attraction that brings them together.
But, restricting to electrons and positrons, what is the property that causes them to annihilate? What is the rule that says when matter and anti-matter meet they annihilate each other?
 A: In the context of Quantum Electrodynamics you can show that electrons (as well as positrons, the antipartner of the electron) couple to photons.
That means that an electron can emit a photon, for example when it is accelerated (see Bremsstrahlung.
Now, you often hear that mathematically it is equivalent whether an electron travels forward in time, or a positron traveling backwards in time. On the level of Feynman diagrams this looks like this.
So instead of having one electron that emits a photon, and continues to exist, you can also have a process as in this diagram. You see that the electron line is preserved. From the model of QED, one can derive a set of Feynman rules, that describes all possible interactions you can have in your theory. One of these rules is that this electron line (the line with an arrow, not the wiggly line) never just stops. Thus, the interaction where an electron and positron run in each other (and annihilate themselves) is allowed.
More generally, all particle-anitparticle pairs can annihilate each other. Since QED preserves charge, it directly follows that particle and antiparticle have to have opposite charges. Also, other quantum numbers have to be opposite.
A: All elementary particles and their composite particles have to obey quantum mechanical equations. all elementary particles have assigned from experimental observations specific quantum numbers , as seen in this table:

Conservation of quantum numbers is at the basis of allowing or not annihilation when matter meets antimatter. As the quantum mechanical solutions of the problem are probabilistic, there is always a probability for matter to be exactly on top of antimatter. If all quantum numbers add up to zero, an annihilation is allowed.
Example, the temporary positronium particle which electromagnetically is like the hydrogen atom, except that it has a probability to decay because the quantum numbers add up to zero. The hydrogen atom is stable , because the electron cannot annihilate  on one of the proton constituents because it has lepton number, and there is no negative lepton number in the proton to allow for annihilation.
