The two major physics discoveries of the first part of this century, quantum mechanics and Einstein's theory of special relativity present new challenges when treated together. The energy ``uncertainty'' introduced in quantum theory combines with the mass-energy equivalence of special relativity to allow the creation of particle/anti-particle pairs by quantum fluctuations when the theories are merged. As a result there is no self-consistent theory which generalizes the simple, one-particle Schrödinger equation into a relativistic quantum wave equation.
The most successful approach to this problem, developed in the early 30's, begins not with a single relativistic particle, but with a relativistic classical field theory, such as Maxwell's theory of electromagnetism. This classical field theory is then ``quantized'' in the usual way and the resulting quantum field theory realizes a consistent combination of quantum mechanics and relativity. However, this theory is inherently a many-body theory with the quanta of the normal modes of the classical field having all the properties of physical particles.
The resulting many-particle theory can be relatively easily handled if the particles are heavy on the energy scale of interest or if the underlying field theory is essentially linear. Such is the case for atomic physics where the electron-volt energy scale for atomic binding is about a million times smaller than the energy required to create an electron positron pair and where the Maxwell theory of the photon field is essentially linear.
However, the situation is completely reversed for the theory of
the quarks and gluons that compose the strongly interacting
particles in the atomic nucleus. While the natural energy scale
of these particles, the proton, 
meson, etc. is on the
order of hundreds of millions of electron volts, the quark masses
are about one hundred times smaller. Likewise, the gluons are
quanta of a Yang-Mills field which obeys highly non-linear field
equations. As a result, strong interaction physics has no known
analytical approach and numerical methods offer the only
possibility, at least at present, for making predictions from
first principles and developing a fundamental understanding of
the theory.
This theory of the strongly interacting particles, quantum chromodynamics or QCD, is especially interesting because the non-linearities in the theory have dramatic physics effects. One coherent, non-linear effect of the gluons is to ``confine'' both the quarks and gluons so that none of these particles can be found directly as excitations of the vacuum. Likewise, a continuous ``chiral symmetry'', normally exhibited by a theory of light quarks, is broken by the condensation of chirally oriented quark/anti-quark pairs in the vacuum. The resulting physics of QCD is thus entirely different from what one would expect from the underlying theory, with the interaction effects having a dominant influence.