The Collaborative Research Center Transregio 24 (TRR24) "Fundamentals of Complex Plasmas" is focused on nonthermal low-temperature plasmas that become "complex" either by embedded microscopic, electrically-charged, solid particles, which form a strongly-coupled subsystem, or by the presence of negative ions, reactive atoms or molecules interacting with surfaces. The core activities in these subfields were initially used to define two project areas, A: Dynamics and Order Phenomena and B: Reactivity and Surface Processes. By joining the expertise of leading scientists at the Ernst-Moritz-Arndt-University in Greifswald, the Christian-Albrechts-University in Kiel, and the INP Leibniz-Institute in Greifswald, the TRR24 became a highly competitive player in this modern field of plasma research. In the second funding period (2009 – 2013), the TRR24 extended its scientific scope towards atmospheric-pressure discharges and material science by including new projects. At the same time, the links between the research areas A and B became significantly tighter, in particular, by studying plasma processes at the surface of embedded particles or by growing nanoparticles from the gas-phase, and the cooperation between the locations could be further intensified. For the third funding period (2013 – 2017), the TRR24 envisages the refinement of important discoveries and developments made in the second funding period, which leads to the successful completion of the original research objectives. Here, e.g., crystallization dynamics, defect structures or waves will be studied in the transition from clusters to bulk matter, or the role of negative ions in the plasma and plasma sheath, respectively. This strategy will be complemented by a strengthening of application-related research in the field of nanoscience, which comprises simulations and experiments on processes in metal-polymer composites, the study of the early growth phase of nanodust, the formation of nanodust in atmospheric-pressure discharges, or experiments on the confinement and dynamics of nanodust clouds in magnetized plasmas. A new focal point has been identified in the important role of surface charges. Here, a thorough microscopic theory of surface charges will be combined with experiments on breakdown development in dielectric barrier discharges, pattern formation, force measurements near surfaces, and dust-particle charging. A second focal point concerns the deeper understanding of strongly-coupled systems in the presence of strong magnetic fields, by ion-streaming effects, or under the influence of rotation. The strategic goals of the third funding period are expected to stimulate the long-term evolution of our field of research.