Trust is a central pillar of the scientific enterprise. Much work in the philosophy of science can be seen as coping with the problem of establishing trust in a certain theory, a certain model or even science as a whole. However, trust in science is threatened by various developments. With the advent of more complex models and the increasing usage of computer methods such as machine learning and computer simulation it seems increasingly challenging to establish trust in science. How and on what basis can an appropriate trust in science be founded?  Should it be only for experts or also for a wider public? Which role do computational methods play in establishing or eroding trust? In this volume scientists from many backgrounds offer their answers to these questions.