The IMPACTS project aims at an ever-increasing integration of modeling, numerics and control design for complex multi-physical implicit systems described by both ordinary and partial differential equations. This integration is achieved considering the novel class of Implicit port Hamiltonian (PH) Systems, analyzing their system properties and developing new dedicated methods for numerical simulation and control design. Implicit PH Systems arise from the modeling of systems with non-local constitutive relations, implicit geometric discretization in time and space or control by interconnection. The methodological contributions of this project will concern the modeling and control of implicit PH systems using irreversible Thermodynamics, geometric numerical methods for space-time discretization and order reduction, canonical implicit discrete-time PH systems and energy-based control design, and in domain/boundary control of distributed parameter systems under implicit interconnections.