In science communication practice and policy, addressing perceived shortcomings in public trust in science has become a guiding star, even a primary purpose. The discourse around public trust in science presents it as a problem than can be fixed. But already in the early 2000s, there was sceptical commentary on this view, on trust’s supposed decline and its possible repair. The prevailing idea of trust makes it barely distinguishable from faith or belief. Mistrust is represented as the polar opposite or as the absence of trust. However, the binary of trust versus mistrust or distrust is being challenged in recent research, notably on political trust. This chapter draws attention to the persistent prescriptive approach to the issue of public trust in science commonly stated on these lines: public trust in science is low and/or declining and science communication has the capacity and responsibility to increase it. We consider how this approach treats mistrust or distrust in science as an aberration, or simply ignores them. There is much space between total trust and determined distrust of science. Individuals and communities may move over time and in changes of circumstances. Moments of selective mistrust can co-exist with a disposition of generalised trust. This chapter presents a scheme of four categories of trust, incorporating—and distinguishing—mistrust and distrust.