Paper is a widely used packaging material and is nowadays regaining importance, e.g., as bio-based and biodegradable material. Moreover, new technologies such as polymer-fiber composites, printed electronics and the deep drawing of paper are developing. The process stability and also the resulting quality of paper converting processes such as coating, metallization, printing, and the printing of electronics are highly affected by the hygroexpansion of paper. In order to reduce production instability and to choose and develop paper substrates with ideal characteristics, critical parameters need to be known. This paper offers an extensive overview of those parameters, starting at a molecular and microscopic level with the effect of the constituents and morphology of single fibers, before moving on to paper contents, chemical modifications and additives and finally concluding with paper production and fiber network modification. It was found that the major influences are single fiber sorption, inter-fiber contacts, microfibril angle, fiber morphology (length, width, curliness) and fiber orientation. This review gives new ideas and insights for technologists working in research, development and production optimization of paper-based products.