In this paper we attempt to motivate, define, and resolve the question "What is the effect of dissipation on quantum tunnelling?" The question is of particular interest in the context of tunnelling of a macroscopic variable such as the trapped flux in a SQUID, where we show thai it is crucial to resolve it in the context of tests of the validity of quantum mechanics at the macroscopic level, but it is also relevant to various microscopic tunnelling situations.