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Advances in technology have enabled the collection of data from scientific observations, simulations, and experiments at an ever-increasing pace. For the scientist and engineer to benefit from these enhanced data collecting capabilities, it is becoming clear that semi-automated data analysis techniques must be applied to find the useful information in the data. Computational scientific discovery methods can be used to this end: they focus on applying computational methods to automate scientific activities, such as finding laws from observational data. In contrast to mining scientific data, which focuses on building highly predictive models, computational scientific discovery puts a strong emphasis on discovering knowledge represented in formalisms used by scientists and engineers, such as numeric equations and reaction pathways. This state-of-the-art survey provides an introduction to computational approaches to the discovery of scientific knowledge and gives an overview of recent advances in this area, including techniques and applications in environmental and life sciences.