We study non-linear σ-models and Yang-Mills theory. Yang-Mills theory on the ν-dimensional lattice ℤ^v can be obtained as an integral of a product over all values of one coordinate of non-linear σ-models on ℤ^v-1 in random external gauge fields. This exhibits two possible mechanisms for confinement of static quarks one of which is that clustering of certain two-point functions of those σ-models implies confinement of static quarks in the corresponding Yang-Mills theory. Clustering is proven for all one-dimensional σ-models, for the U(n) ×U(n) σ-models, n=1, 2, 3, ..., in two dimensions, and for the SU(2) × SU(2) σ-models for a large range of couplings g² ≳ O(ν). Arguments pertinent to the construction of the continuum limit are discussed. A representation of the expectation of Wilson loops in terms of expectations of random surfaces bounded by the loops is derived when the gauge group is SU(2), U(n) or O(n), n=1, 2, 3, ..., and connections to the theory of dual strings are sketched.