The application to Biology of the methodologies developed in Physics is attracting an increasing interest from the scientific community. It has led to the emergence of a new interdisciplinary field, called Physical Biology, with the aim of reaching a better understanding of the biological mechanisms at molecular and cellular levels. Statistical Mechanics in particular plays an important role in the development of this new field. For this reason, the XXth session of the famous Sitges Conference on Statistical Physics was dedicated to "Physical Biology: from Molecular Interactions to Cellular Behavior". As is by now tradition, a number of lectures were subsequently selected, expanded and updated for publication as lecture notes, so as to provide both a state-of-the-art introduction and overview to a number of subjects of broader interest and to favor the interchange and cross-fertilization of ideas between biologists and physicists. The present volume focuses on three main subtopics (biological water, protein solutions as well as transport and replication), presenting for each of them the on-going debates on recent results. The role of water in biological processes, the mechanisms of protein folding, the phases and cooperative effects in biological solutions, the thermodynamic description of replication, transport and neural activity, all are subjects that are revised in this volume, based on new experiments and new theoretical interpretations.