Preface of the special issue on mathematical and computational modeling in biomechanicsBiomechanics is one of the fastest growing areas of mechanics research. While less than 1000 researchers participated in the 3 rd World Congress on Biomechanics in 1998, more than 4000 participants were counted at the 8 th World Congress on Biomechanics held in 2018 in Dublin, which makes biomechanics nowadays one of the largest research communities in the area of mechanics. The fast rising number of scientists working in biomechanics is in the first place the consequence of a change of paradigm that has taken place in life sciences mainly over the last three decades. For centuries, biochemistry was considered the primary subject area for understanding the functioning of living organisms. However, the recent rise of mechanobiology has revealed that many of the most fundamental mechanisms in living organisms are in fact not -or at least not exclusively -controlled biochemically but rather mechanically. Unraveling the role of mechanics in living organisms has proven to be highly rewarding but also highly challenging. In particular, due to ethical concerns and the inherent complexity of living organisms, experiments in biomechanics usually take much more time and resources than in classical mechanics. Mathematical and computational modeling can be the key for reducing experimental efforts. Developing and using this key can be expected to be one of the most promising areas of research for investigators in mechanics and applied mathematics over the next decades. This special issue in ZAMM seeks to cover the whole range of questions and problems in biomechanics from fundaments to clinical research.Given the above-mentioned key role of mechanobiology in the fast rise of biomechanics over the last decades, it is natural that many of the articles in this special issue focus specifically not only on mechanical aspects alone but rather on the interplay between mechanical and biological processes, that is, on mechanobiology in the broadest sense. In this special issue, the two probably most prominent sub-areas of mechanobiology are addressed, which are mechano-regulated growth and remodeling of biological tissues and electrophysiologically and biochemically controlled muscular contractions. Within the area of mechanoregulated growth and remodeling, the review article [1] focuses on the cellular and sub-cellular foundations, in particular on cellular mechanotransduction and contractility. These phenomena translate on the tissue scale into characteristic mechano-regulated growth and remodeling processes.[2] and [3] propose novel mathematical models for these processes in arteries. Such models always rely not only on information about the cellular foundations of mechanobiology but also on a detailed understanding of the mechanics of soft biological tissues, which is crucially governed by their fibrous microstructure. Understanding the role of this microstructure during macroscopic tissue deformations remains an ongoing area of research that i...