QED can be seen as a part of a larger theoretical model called
the ``standard model'' of electromagnetic, weak and strong interactions.
The standard model was developed during the sixties and the seventies
and accounts for a large variety of phenomena: for instance, the fact that
due to the weak interactions,
the muon, a particle similar to the electron but approximately
200 times heavier, decays in average after 
, and how
the strong forces bind
three quarks into a proton of a size which is roughly 
.
Some of its crucial predictions (the existence of the Z and W particles,
and of the top quark)
were verified between 1983 and 1994.
However, in 1998
important theoretical and experimental aspects
of the standard model remain to be understood. See chapter 4 of QED.
During the last decades, many particle physicists have attempted to build unified theories, where the electromagnetic, weak and strong interactions follow from a single type of force or principle. Gravitational forces were also involved in more ambitious schemes which would explain all the known interactions. However, reputable physicists strongly disagree on the issue of a Theory of Everything (see appended material).
Symmetry is an important aspect of several of the theories mentioned above. Indeed, it seems that whenever one tries to understand natural phenomena at shorter distance, the symmetry increases. In physics and mathematics, the word symmetry has a definite technical meaning: it means that some object remains unchanged after a certain transformation.
For instance, there is no difference between a given square and the same square rotated clockwise by 90 degrees about an axis perpendicular to its surface and passing by its center. We then say that this square is invariant under this rotation, or that this rotation is a symmetry of the square. In addition, if we perform this rotation two consecutive times, we obtain a transformation which could have been obtained by rotating the square once by 180 degrees. We can also ``undo'' clockwise rotations by performing the corresponding counterclockwise rotation. The set of rotations which leave the square invariant form a group with four elements. In this special case, it does not matter in which order two transformations are performed. You can work out the symmetry group of the cube. You will find that this group has 24 elements and that in some cases the order in which you perform two transformations matter. This difference between the symmetry group of the square and the symmetry group of the cube is crucial to understand the difference between the electromagnetic and the strong interactions!
There exists a deep connection between the symmetries of a physical theory and conservation laws, i.e., the fact that some some quantities remain constant during the time evolution. The most familiar example of a conservation law is probably the conservation of energy, which indeed is a consequence of the symmetry under a change of origin in the time variable (i.e., we can choose arbitrarily which instant is called time 0). The connection between these two features is called Noether's theorem and is difficult to explain at an elementary level.