This volume presents recent advances and open problems in the cross section of infinite-dimensional systems theory and the modern treatment of PDEs. Chapters are based on talks and problem sessions from the first “Workshop on Systems Theory and PDEs” (WOSTAP), held at TU Bergakademie Freiberg in July 2022. The main topics covered include:Differential algebraic equationsPort-Hamiltonian systems in both finite and infinite dimensionsHighly nonlinear equations related to elasticity/plasticityModeling of thermo-piezo-electromagnetism