Complex systems theory emerged as a part of science aimed to describe collective properties of large aggregates and spontaneous formation of macroscopic systems whose features become fairly independent of many details of the microscopic dynamics. Complex systems are usually characterized by their multiscale interactions among inner constituents, nonlinearity and „butterfly-­‐like“ sensitivity on the choice of initial conditions. They are also inherently dynamic, i.e. pointing to self-­‐adaptive properties of matter. High level of differentaiation in structure and organization on one hand side, and their incipient, evolutionary propensity on the other, call for establishing theoretical tools to explain unusual properties of complexity and possibly, to formulate a unified scientific scheme of their description. The core idea in the theory of complexity lies in their spontaneous symmetry breaking, combined with the emergence of new organized phases and temporal coherence. That observation has led to the engagements in this field many concepts stemming from nonequilibrium statistical physics, theories of deterministic chaos and stochastic processes. Inspiration for further developments in analysis of complexity comes from many diverse domains of human activities, encompassing interdisciplinary research, informatics and systems thinking. The special volume of Acta Physics Polonica B covers mathematical and physical concepts relevant in studies of complex dynamic systems with a focus on open problems and new techniques. The volume has been prepared upon successful dicussion led by the community of researchers involved in two past conference events: Workshop on Dynamics of Complex Systems 2014 prepared and hosted by FINATEC, University of Brasilia and the 27th Marian Smoluchowski Symposium on Statistical Physics 2014, jointly directed with our Brazilian friends. As Guest Editors of the volume we hope that presented selection of articles will not only provide the proof for diversity of subjects encrypted under the word „complexity“, but also bestow a feedback of innovative approaches which could deepen our understanding in this field. The project has been supported by funds from the Marian Smoluchowski Kraków Research Consortium "Matter-­‐Energy-­‐Future", which includes the Faculty of Physics, Astronomy and Applied Computer Science as one of its members, granted the status of a Leading National Research Centre (KNOW). Additionally, Guest Editors acknowledge a financial subsidy from the M. Kac CSRC, UJ. Paweł Góra, Ewa Gudowska-­‐Nowak, Fernando Oliveira. Kraków, June 2015.