This editorial welcomes readers, authors, reviewers and colleagues to the first volume of Applied Mathematics of Interconnected Phenomena, an international, peer-reviewed, open access journal devoted to networks, dynamical systems and complex phenomena. It explains why the journal was created, what kinds of mathematical contributions it seeks, how manuscripts are evaluated through a single-blind process, and which editorial and ethical commitments the editorial board makes to its authors and readers. It closes with an invitation to submit work that connects rigorous theory with computation and with applications in the physical, biological, engineering, economic and social sciences.