This book contains 29 invited articles written by participants of the International Workshop on Operator Theory and its Applications held in Chemnitz in 2017. The contributions include both expository essays and original research papers illustrating the diversity and beauty of insights gained from applying operator theory to concrete problems. The topics range from control theory, frame theory, Toeplitz and singular integral operators, Schrödinger, Dirac, and Kortweg-de Vries operators, Fourier integral operator zeta-functions, C*-algebras and Hilbert C*-modules, to questions from harmonic analysis, Monte Carlo integration, Fibonacci Hamiltonians, and many more.The book is addressed to both researchers in operator theory and researchers in various applied fields, such as physics, engineering, or numerical mathematics. The former ones will find open problems from applications that might stimulate their work, while the latter ones will learn how to use the potential of operator theory for tackling interesting practical problems.