Two-dimensional antiferromagnets are the precursor insulators of high-temperature superconductors. At low temperatures $T$ the $(2+1)$-d antiferromagnetic spin 1/2 quantum Heisenberg model reduces to the 2-d classical $O(3)$ nonlinear $\sigma$-model, which is in many respects similar to QCD in four dimensions. In particular, in the limit $T \rightarrow 0$ the correlation length $\xi \propto \exp(2 \pi \rho_s/T)$ diverges due to asymptotic freedom. Consequently, the extent $\beta=1/T$ of the Euclidean time direction vanishes in units of $\xi$, and the system undergoes dimensional reduction. In complete analogy, 4-d QCD is obtained via dimensional reduction of a $(4+1)$-d quantum link model. Quantum links are the gauge analogs of quantum spins. Like the link variables in Wilson's formulation of lattice QCD, quantum links are $3 \times 3$-matrices. However, their elements are non-commuting operators acting in a finite Hilbert space. The quantum link formulation of QCD is promising both from an analytic and from a numerical point of view. Also other field theories arise naturally from the {\em dimensional} reduction of {\em discrete} variables. The resulting non-perturbative {\em D-theory} formulation of quantum field theory shares several interesting features with M-theory --- the non-perturbative formulation of string theory.