This book is focused on the simplest of the iron-based high temperature superconductors, namely the binary iron chalcongenide family. Compared to the other families, it consists of a stack of FeCh layers only. It is considered an ideal modeling system for the other iron-based superconductors due to its simplicity and its similarity with their electronic structure. The electronic phase diagrams of the FeCh family contain the appearance of different ground states. Whereas the mother compounds are in general antiferromagnetically ordered, the material becomes superconducting after going through a region where superconductivity and magnetism coexist. In the framework of this book, the FeCh system was tuned solely by changing the lattice either by hydrostatic or chemical pressure and without introducing additional charge carriers. The muon spin rotation/relaxation/resonance technique in combination with ac and dc magnetization experiments is an ideal tool to investigate the superconducting and magnetic states and the interplay in a sense of competition and/or coexistence between them.