  We review some recent results related to the notion of volume independence in
SU(N) Yang-Mills theories. The topic is discussed in the context of gauge
theories living on a d-dimensional torus with twisted boundary conditions.
After a brief introduction reviewing the formalism for introducing gauge fields
on a torus, we discuss how volume independence arises in perturbation theory.
We show how, for appropriately chosen twist tensors, perturbative results to
all orders in the 't Hooft coupling depend on a specific combination of the
rank of the gauge group (N) and the periods of the torus (l) given by l
N^{2/d}, for d even.We discuss the well-known relation to non-commutative field
theories and address certain threats to volume independence associated to the
occurrence of tachyonic instabilities at one-loop order. We end by presenting
some numerical results in 2+1 dimensions that extend these ideas to the
non-perturbative domain.
