Zamolodchikov's c-theorem showed how flows of couplings under renormalisation in two-dimensional quantum field theories are constrained by a gradient flow equation with a positive definite "metric", leading to a "c-function" monotonically increasing with energy. The a-theorem is the extension of this result to four dimensions; it is now well-established that a similar result holds, at least perturbatively, in all even dimensions. In this talk we present "experimental" evidence for similar behaviour in three-dimensional theories.